Cut and edit the list as you see fit, I'm interested to know what would be a more solid guideline than just making an ad hoc list, some make sense, some are maybe.
As you wish.
Feat (Prerequisite)
Alert (none)
Yes.
You skipped "Athlete", which is just as well since it's a "no." Your body and movement, in my book/game, are the animal's. Your athleticism in your normal form does not translate.
Actor? Sure. Ok. It's Cha. based, you get to keep it. Obviously, the "mimic speech/animal sounds" feature can't be used unless you are an animal that can mimic speech/sounds, such as a raven, parrot or magpie, a hyena could laugh, a goat could scream, etc...
Specifies the use of a melee weapon, so no to that. I would probably be inclined to rule the "shove" use of the feat (provided you were an animal of some size/bulk) was ok.
Wis. & Int. dependent. This is a yes/fair game.
Grappler (Strength 13 or higher) - If Wildshape form has Str >=13, and maybe the grapple action/attack
Right. If the animal has the strength and means to grapple or, like, a constrictor snake or something that specifies a grappling attack in the animal's stat block, then fine.
Inspiring Leader (Charisma 13 or higher)
Ohhh, I see now, you already eliminated all of the weapon dependent ones. Good man.
Inspiring Leader...mmmm, it is Cha. dependent...but I would say it requires speech, "inspiring your companions, shoring up their resolve...". Yeah, I'm gonn amake this the exception to the Int/Wis/Cha "rule." This will be a no at my table.
Yeah. No problem here.
Can't speak. No.
Sure. I don't see why not.
This gets split, like Charger. The first feature specifies the use of a melee weapon, so, no. The second feature, imposing disadvantage on the concentration save from the damage you inflict...yes. Advantage to spell saves, also, I see no reason would change.
Martial Adept (none) - If Wildshape form has physical characteristics to perform maneuver?
The wildshape having the form to perform the maneuver is not as important as the fact that most of the maneuvers are melee weapon attacks. In fact, a quick once over the Battlemaster maneuvers shows nearly every one is the result of you making "a weapon attack" or "melee weapon attack". The feat is based on using the BM maneuvers and the BM maneuvers are based on the assumption that you are attacking (whether you hit or not) with a [unspoken] "wielded" weapon. The few that don't are so corner that, for simplicity's sake, I'm just going to say this is a No.
For me, this is a no. For Remathilis' table, this is a yes (even though 5e is fairly clear in limiting/eliminating "stacking"). SO this is really a call you have to make...and stick to. You can move faster in your normal form...when you become an animal, you take on THEIR movment rate...to say you automatically "fly faster" than other eagles when you turn into an eagle or "slither through tight spaces faster" as a salamander just doesn't sit right with my immersion spidey senses[tm]. So I say this is a no.
Wis/Int based. So yes.
Resilient (none) - If Int, Wis, Cha chosen as stat
Right. Yes for Int. Wis. Cha. No for Str. Con. Dex.
Specifies "melee weapon attack", so no.
Add it to the Charger list. The first two features (about OAs) are fine. The "reaction to make a melee weapon attack" within 5' of you doesn't fly. So this is split.
You are using a ranged weapon how? No dice.
Would dependent on what the skills or tools were. Let's try to follow our own system and just say "Int/Wis/Cha" based skills, sure. "Str/Con/De" based skills, unless the animal has proficiency with it, no. Obviously, no one in animal form are using tools...unless, maybe they are a chimpanzee.
Skulker (Dexterity 13 or higher) - If Wildshape form has Dex >=13
Right. Yes, if the animal form has >=13 Dex.
War Caster (The ability to cast at least one spell) - If Druid cast a concentration spell prior Wildshape form (e.g. call lightning)
I would rule, if you want to insist, that they can have the advantage to Con. saves to maintain concentration. Fine. The other two features, obviously are non-starters.
So, like I said, whatever makes sense and/or your table/houserules agree.