My attempt to reply with quote was destroyed via. the formatting of the OP. Do not quote the OP.
Bonus Feat: I would suggest not giving out the double proficiency part of the Feat, because it will make skill checks far too easy (and step all over the Rouge & Bard).
Classes: the Monk has d8 HD because it’s not a true warrior, but more of a skirmisher (like the rogue). Some might argue the same about the Ranger, but Ranger has been considered part of the warrior group since the beginning.
Spells: Concentration is a pain for many players, but there is a reason for it. You’ve already noted that Invisibility and Fly can combo with things horribly. I’m positive you will find more combinations that you hate if you relax Concentration.
Spells: I normally use an Intelligence/Arcana check instead, but an additional save works just as well.
Long Rest: I’d add the ability to spend HD at the end of the rest, otherwise every Long Rest will be immediately followed by a Short Rest to regain necessary HP.
Skill Checks: requiring proficiency (except for tools) goes against the philosophy of 5E. I know that multiple checks among the party is a pain and needs fixed, but I don’t think this is the way to do it. Also, please note that players CANNOT call for ability checks, ever. Only the DM may call for it (since sometimes you don’t need a roll, because it’s too easy or impossible).
Death Saves: like the idea, but be ready for a lot more character death. Don’t forget that any damage deals 1 Failed Death Save (2 for a Critical Hit).
Exhaustion: I would consider putting a limit on the amount of exhaustion gained, because you can only get rid of 1 per Long Rest (short of a 5th level spell). I’d suggest allowing 1 level of “Dying Exhaustion” to be removed per Short Rest in addition to the normal reduction.
Accelerated Recovery: very bad idea! As a cantrip, this basically removes 90% of the purpose of a Short Rest. In combat, it’s probably fine, but out of combat a short rest can be taken in only a minute or two (at least for HP purposes).
Sorry that my formatting screwed up quoting, but thanks for fixing it. Anyway on to your comments:
Bonus Feat: I do like the idea of just giving them the skill proficiency (not expertise) and the additional usage of the skill
Monk: I haven't played a monk personally but a friend of mine seemed like he always had a hard time, but that was also before he realized stunning strike (we were lv 9 before he used it lol). So, yeah it probably is fine at a d8.
Spells: The main reason I want to allow concentration on two spells is to allow those low level spell (bless, fog cloud, faerie fire) to be relevant at higher levels. So to instill that idea a little bit better here is variant idea: The pc could concentrate up two spells at once, whose total spell levels aren’t greater than the highest spell slot you can cast. I feel this give a little bit of flexibility without breaking the game. For instance if the pc wanted to cast fly (3rd lv spell) and invisibility (2 lv spell) they would have to have a 5 lv spell slot, but they wouldn't be able to concentrate on two spells if they wanted to cast Dominate Person (5th lv spell)
Long Rest: Agree meant to add that.
Skill Checks: This could be more how our group plays, but if character wishes to investigate a device but fails. Then another pc would step up and try it. If you have a group of 5 chances are at least one person would pass the check even if that arent proficient in the skill.
Death Saves: We don't have enemies continuously attacking pc that have fallen "unconscious". I just used this rule because most of the time someone would be fine after three rounds but no one checks on them or the crit fail then the party rushes to them. This is mostly to prevent meta-gaming.
Exhaustion: Adding exhaustion was to prevent they are healed 1hp rush into combat. Downed in one hit and healed 1hp (I'm guilt of doing this as well). Although this doesn't happen too much with my group we tend to forget that retreating is an option. I would say you could remove a lv exhaustion for 1 hit die during a short rest.
My intention is to make the hit die more useful in different scenarios but keeping it a limited resource.
You can only gain the short rest effect (resetting abilities for fighter, warlock, etc) if you can spend a hit die
You only gain hit die from long rest, which then requires spending them or healing from some other means
You can spend 1 hit die to remove a level of exhaustion gained from dropping to zero
Accelerated Recovery use you could use the cantrip and heal everyone to their max (baring they have the hit die), but they can not benefit from the short rest effect.
Everything but what happens at 0 HP makes the game much easier. 5e isn't particularly in need of boosting PC strength.
I do like the "gain exhaustion at 0 HP" as I implemented it in my campaign a few months ago when I proposed it to my players and they said they liked it. Yes, they voted to make things harder for themselves.
I also like the "don't death save until someone checks on you". I haven't seen that one suggested before. If I ever get to play a PC some time I'll be sure to ask the DM to implement it.
I known in 5e you really don't need to increase the strength of the pc, but I always like to add a rule to try and make something that was weak relative.
That's a lot so I'm just gonna comment on one thing at a time. Well, the stuff that interests me.
If you're up for a bit more work, I have an idea to enhance this. Rather than giving the wizard "1 + wizard spell (except fly and invisibility) assign a specific spell to each wizard school and make it "1 + school spell."
You might then even be willing to give the Illusionist invisibility because it enhances their niche.
I do like the thematic of it. That you specialize in a school which allows you concentrate on two spell, but I think that would really push certain traditions to be more useful than others.