Okay, so I'm finally at a computer so I can type a bit better than on my phone.
I'm going to start with the assumption that feats should be worth +2 to an ability score. The problem is not all ability scores are really equal, nor are all ability scores equal for every character (Con is useful for everyone, Dex is useful for most, Wis is pretty useful because of the ubiquity of Wis saves ...). Every ability score comes with Bonus to hit/DCs and sometimes damage, but not every character can tap into these. Okay, well that's fine. We can still use that to say that, since Con is +1 hp/level and +1 con save (and some random con checks or round timers), it's fair to say that +1 hp/level is worth half a feat and thus Toughness is an okay feat (not the best, no one's going to do a backflip to take it, and I'd argue that it's slightly weak since Con also improves HD rolls, but that's kind of part of another discussion).
One problem is the inclusion of combat feats among non-combat feats. I really think the game could have benefited strongly with separating these. Alternatively, combat feats could have been about the creation of options rather than strict power gains (like learning new cantrips or spells, and trade off maneuvers for weapon combat). Maybe we can save that for 6th Edition.
CHANGELOG- VERSION 1.0 - Blue is correction - Green is improvement - Red is nerfed
Athlete
Added advantage against exhaustion caused by strenous activity, because this needed some improvement,
I probably would have baked a bunch of those effects into skill checks. Then I'd just lump this into an Expertise feat where you get +1 to an ability score and training or expertise in a skill.
Actor
No changes. Still weak, I feel. Input appreciated.
I don't this this is weak, just highly situational. I don't play intrigue focused games (I don't think the system is good for it). But, again, the mimicry could be a skill check and advantage could be replaced with expertise for that earlier feat idea.
Charger
Added scaling damage to the attack, or knock prone to the shove. Feels this makes this feat more worthwhile.
Definitely needs scaling. A prone on the shove would be nice too; +5 feet really doesn't feel like much (I think the amount you shove someone should already be a function of your opposed strength check).
Crossbow Expert
Added 'made with a crossbow' to second feature, to avoid abuse (applying it to spell attacks or other ranged attacks).
I see where you're coming from, but I don't see a spellcaster spending a whole feat to get that one effect. Limit this feat, but add in a feat to get this (I'm really surprised it's not part of warcaster).
Defensive Duelist
Added a riposte attack, if the bonus causes your foe to miss you. This makes the feat more worthwhile, in my opinion.
You felt this feat was weak? It feels like a situational, at-will, nerfed Shield spell. My only issue with it is that it doesn't synergize with the rogue's Uncanny Dodge, and they're the class I would most expect to pick up this feat.
Dual Wielder
You now make your off-hand attack as a part of your attack action. You are still limited to one off-hand attack per round (unless you use Action surge, in which case you can now make two). This makes TWF more viable at higher levels (which it needed), and even better for a rogue (possibly an issue).
So, I'm a big hater on the current way TWFing works. This fix still only amounts to +1 to damage per attack and +1 AC. Yes, not costing a bonus action would help a lot of builds, so that's where it's real strength would lie (as it would stack with action surge, be usable with martial arts, be usable with cunning action, be usable alongside rage and bonus action spells ...). I'd prefer to not fix TWFing with a feat, though, and I really want to see TWFing not cost a bonus action since the other styles don't.
Durable
Added advantage on death saving throws. Still weakish, but this brings it up a nudge.
I've been convinced to just get rid of it, and to have Toughness also heal +2 HP on every HD rolled. That way Toughness is more equivalent to half of Constitution, and no more feat that does nearly nothing for some characters (and a ton for others).
Elemental Adept
Added a reactionary damage resistance. I hate doing this, because I think that the way 5E is doing it (vulnerability/resistance) is really good, and this adds unnecessary complexity. But straight resistance is too strong, I think.
Xanathar's has a feat, "Infernal constitution" that grants +1 Con, and 2 resistances, and advantage on saves against being poisoned. I don't think they value resistance quite so much. Armor of Resistance is a rare item, though, so maybe this is just racial feats having more oomph. Reaction resistance is part of the Absorb Elements spell, but you've weakened it considerably.
Grappler
Second feature removed as per the errata, but added an opportunity to grapple larger foes at a disadvantage. This makes the feat worth a grab, for the dedicated grappler.
I don't think anyone is going to succeed on grabbing a large creature if they have disadvantage; large creatures tend to have higher strength. With the right tools, regular people can grab and hold still large animals (lassoing or holding the reins of a horse, for instance), so I'd be happy with the feat letting people grab large creatures (maybe not pin them, I don't know, beowulf wrestled grendle).
Great Weapon Master
Changed -5/+10 to -3/+6. This reigns in the feats power level slightly, while not completely devaluing it. I feel this is a needed balancing act.
+10 damage is way too much at first level and I've seen that happen twice with human barbarians. It feels like too much damage at 5th level with Extra Attack too. So I agree with you. I want to see it tied in with Proficiency bonus though; give up your proficiency bonus to hit and apply double your proficiency bonus to damage.
Healer
No changes, but could use a buff, I think. Input appreciated.
God, it could use a nerf. Over the course of a day, if you only used it on yourself, this feat offers more HP than Toughness does, and we established that toughness is a relatively balanced, if boring, feat. And you can use it on the whole party. I'd make it take longer than a round and buff the raw healer's kit and just accept that the healer's kit is part of the adventuring resources so they can actually get through those 6 to 8 medium encounters per day. =)
Heavily Armored
No changes, but could use a buff, I think. Input appreciated.
No buff, I think it's fine. It's +1 AC for someone with a Dex 14 and Medium armor, and more if you have lower Dex. Plus it's a half feat. +1 AC feels like half a feat to me (don't look at me Dex, you're an overpowered stat but it's only okay because medium and heavy armor characters don't use you as much).
Keen Mind
Added advantage on Intelligence (Investigation) checks that require attention to detail. Slight improvement, but probably still a weak feat.
Again, make these functions of skill checks and introduce that Expertise feat.
Lightly Armored
No changes, but still kinda weak.
This is +2 AC (studded leather) for characters without armor proficiency. This is the wizard, right? The wizard could spend a spell slot on Mage Armor, and Elven Chain isn't super rare. It's boring, but it fits into my view of feat balance.
Linguist
Added advantage on Insight checks to understand unknown languages. Still kinda weak though.
Considering you can learn languages in downtime now, that comprehend languages is a first level ritual spell, I'd be more than happy to let the "Linguist" character know basically all the languages (like all the languages of the PC races) and checks to learn rarer languages.
Magic Initiate
No changes, already strong.
I actually would like to sit down and investigate this. Spell Sniper shows that learning a cantrip isn't worth a full feat. If the 1st level spell 1/day is worth a half a feat, I really don't think it is. Look at the healer feat vs. Magic Initiate with cure wounds. Look at the value of using that spell slot for Smite (not sure if you could, but just to get an idea of how much power this feat is giving); that's +2d8 damage, per day. You've already said that you thought Martial Adept needs an extra die. If baseline hit chances are around 65%, then +1 to hit is about a 8% increase in damage, on every attack across a day. Damage scales with level.
Magic Initiate needs a buff. At minimum, it should be a slot that is regained on a short or long rest. At best, the slot should grow in size based on your level. I can sit down and do the math on it later, it's on my to do list.
Martial Adept
Increased the number of dice from 1 to 2, to make this more worthwhile.
I agree this needs to be looked at. I think the Fighter gets too many dice at 3rd level compared to what the Eldritch Knight gets, and I think class abilities at a level should be worth around a feat because of the way the MC system works (which is a reason I don't like Extra Attack being part of class progressions), but my Battle Master rewrite has 2 dice at 3rd level so I think that would be fine for a feat (plus it's smaller and it teaches less maneuvers).
Moderately Armored
No changes, but still kinda weak. Input appreciated.
I think it's fine. For low Dex characters, it's an AC boost, plus you get a shield which is even more of an AC boost.
Polearm Master
Now includes spears as well (because if you include quarterstaves, you really should include spears!) Also fixed in accordance with Crawford ruling, to only allow OA's from the polearm.
I would probably also require that quarterstaff and spear should only work when they're being wielded two-handed. Holding a spear in one hand and whacking someone with the backside of it is stupid, and if you're going to allow that then I want to be able to skull bash people with my sword pommel as a bonus action.
Savage Attacker
Added a Strength bonus. This makes the feat more par for the course.
I feel like it's still not that much, but it definitely helps.
Sentinel
Added check if the creature is larger than you. Please, no more stopping dragons with ease.
I don't think the feat is overpowered, but a check seems fair for this. Like, imagine a fighter hitting the tarasque with an OA and it stops ...
Sharpshooter
Changed -5/+10 to -3/+6 proficiency. Same reasoning as GWM.
I vote -Prof/+2xProf. But, I don't like that it can be done with hand crossbows. Power Attack used to be - to hit/+ to damage, and the damage was doubled for two-handed. That kind of goes for stacking GWM on top of Polearm Master's bonus action. I don't like it.
Skilled
Changed a lot. You now get a bonus to an ability score, and proficiency/expertise in a single skill, instead of proficiency in three skills. I feel that people would very rarely feel the need for 3 proficiencies, so this feat gets overlooked because people feel parts of it is a waste ("eh.. I want stealth, and I guess I'll take acrobatics and.. uh.. Persuasion too.."). This way, I think it's less wasteful.
I'm with you. Are you saying proficiency and expertise, or "or"?
Weapons Master
Increased to all martial weapons, because this feature needs less restrictions, not more. In an ideal world, I think this should be combined with the armor feats in a way that would make them more useful. I'll think on it.
What, pair simple weapons with light armor and pair martial weapons with heavy armor? (Medium gets shields)?
Since I cannot think of any class, except maaaaaybe the cleric, who don't have martial weapons who would gain benefit from martial weapons, and have abilities that use weapons (so life, maybe nature if they didn't pick up shillelagh, and trickery), I'm not concerned with mixing these. Martial weapons are, for the most part, +1 damage over their simple counterparts. If you only have 1 attack, I'm not concerned with this, and everyone with extra attack already has martial weapons or doesn't need them (monk).
Hope those thoughts help!