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Rogue Hiding:

What about having a miss cause you to have to roll a new hide check with disadvantage (or grants the target advantage on spot, whichever way feels better) as a rogue and a hit auto makes you seen. For other character either result makes you visible. Or Maybe if you want to be nicer to rogues (only, or other rogue-like classes Ranger, Assassin, etc. that develop later) then have the system work like this:

While hiding if you make an attack: you must roll another hide check after attacking with disadvantage, if you hit anyone that sees the attack land gains advantage to perceive/find you.

This would make you really easy to find on hits, and slightly easier to find on misses. (Sort of like the old -20 to hide checks in 3rd ed.)

Fighter Modifier Damage on Miss:

As for the fighter deals mod damage on a miss, I really disliked that in 4th edition and now 5th but my players really like it a lot (my players hate 4th for reference, I don't mind it as a DM), so I'm not sure what to say about that other than fun is the key determining factor to me. If you want another option; what about making a natural 1 still misses but otherwise a miss deals damage modifier damage (for fighters with that ability). If you really want it more tough then maybe make the player roll a 2nd time (if the first misses) and if that hits then it deals modifier damage (if not it misses completely).

Criticals Max Damage:

Max damage for criticals (not sure if this was implied) seems fine to me because in 3rd (my group's preferred edition) it got pretty scary with critical hit multiplies and insane modifiers getting multiplied (throw in charge and even sillier results ensue)

Touch AC:

I really like touch AC but holy crud did that and flatfooted take a while to explain to new players (especially with all the modifiers), and took time in game especially when 1 or multiple modifiers needed to be removed or added to alternate types of ACs as things happened in combat. However for the more experienced players in my group I loved how touch AC allowed me as a DM to describe a throwing axe sticking into someone plate armor or shield because it missed the players AC but hit touch, or when having other players stand in front to block shots, saying they can't dodge/avoid the attack or it hits their ward but flatfooted AC is fine.

D20-Variance:

I think the variance on the D20 is a bit high so that’s why people tend to favor large bonuses or auto-hits/effects (I believe there is a whole topic on d20 random variance in these boards somewhere). But because a large part of most abilities (attacks, saves, skills, etc.) require a d20 roll, it becomes possible to become extremely unlucky, I have had this turn out to wreck entire game sessions. So having a miss once or twice when unexpected is fine having it happen more often than that can be un-fun so for that reason I'm not strongly opposed to auto-success if used correctly and sparingly.

Strength Rolls:

I think you guys figured this one out, but I'll just add I never liked the rules being written (I know I could just veto as a DM but...) so that players needed to make strength checks to open doors, lift things, etc. it never really made sense either you are strong enough or not. I usually interpreted the checks to mean that you took a while to maybe preform the task due to it being a little awkward but then I had no real explanation for when the tiny goblin stepped in and lifted the boulder by rolling a 20. So in that sense I like the rules clearly stating when it makes sense don't bother rolling (even though I often did that anyways). On this one I think the DM should be the one that decides if the check is needed or not

In Closing:

Sorry for the long post just some of my random thoughts, I don’t actually feel strongly one way or the other but thought I’d try and provide some possible options.

I’m tempted to just roll a d4 for arm-wrestling (or other similar tasks) to represent the daily wellness of each participant, the current conditions, some minor random luck (when to pull against, etc like minor tactics), etc.

That way you would get: STR 18 (+4) = 1d4+4 {5-9 result} against:
STR 1 as  1d4-5 {0} vrs. {5-9} -- Making it impossible to win
STR 10 as 1d4 {1-4} vrs. {5-9} -- Making it impossible to win
STR 12 as 1d4+1 {2-5} vrs. {5-9} -- Occasionally able to hold against
STR 14 as 1d4+2 {3-6} vrs. {5-9} -- Sometimes tie and rarely win
etc.  

If you think more random factors should apply change my idea to a d6 or d8, like if both contestants are drunk, maybe you think a mental aspect applies, getting in the head of the opponent, etc. add whatever you like. This is essentially a mini-game within the game. It would be like trying to get a perfect representation of a d20 roll for two players playing poker, until you get the cards out it’s only an approximation. Don't feel constrained to a d20 if you don't want the huge variance, or just remove the rolls altogether for things that don't make sense.  The roll covers things that are out of control of the parties like minor weather (random gust of wind), split second strategies (bob left, duck, pull now, tighten grasp, taunt opponent, etc.), luck, conditions (high altitude, crowd cheering you on), wellbeing (Maybe one person is slightly under top condition), minor surroundings (the pebble, dust falling from the ceiling, crack in the wall letting the sun in your eyes), etc. Granted some of those could be controlled and some might be major concerns but you get the idea, so that being said I feel there is still some random factors to even an arm-wrestling match, but that’s just my opinion.