As a rule, ranged fire always deals Strength-based damage, never Dexterity-based damage.
Thrown finesse weapons remain unchanged (they still allow you to use Dexterity for both attack and damage).
I have a houserule similar to yours: I allow either Str or Dex to be used for attack and damage with bows. Technically this actually advantages ranged combat more, but I've found that it doesn't tend to actually play that way. While it gives the Str-based characters an effective ranged option in those few situations where melee isn't an option (such as against flying creatures) the group as a whole still prefer melee or short range combat.
Crossbows present an issue, since it is hard to justify basing their damage on Strength. I'd suggest either increase their base dice or adding proficiency bonus if you wanted to swap out the Dex component.
2a. Lets cap the Dexterity bonus of *any* AC calculation to +2.
Doesn't seem to fit, either thematically or mechanically. You'd probably be better off just giving light armours a Dex cap. Monks and Barbarians are a special case, but bear in mind to approach armoured ACs, let alone surpass them, they are having to max out two different stats. This comes with the commensurate cost in ASIs as opposed to feats. At higher levels this allows a monk to the same AC that a heavy-armoured fighter can. Barbs can go higher, but at the cost of having to put those ASIs into secondary abilities.
Where these are an issue however, is where rolled abilities are used, and one person gets multiple, very high rolls. - But that is a balance issue already.
Perhaps a houserule limiting unarmoured AC bonuses to max of proficiency bonus? While I personally wouldn't apply this to any Dex bonus to AC, you might find that is best.
Heavy Armor prevents you from benefiting from a Speed increase, whether magical or otherwise. A Speed increase can still negate a Speed penalty but that's it.
I'd suggest limiting heavy armour's speed by reducing the movement the Dash action grants by half in heavy armour. This seems to fit better with the idea that a trained fighter can move just fine at a reasonable rate while in plate, but it does limit her ability to put on bursts of speed. I'd also suggest some armours grant disadvantage in Str or Con (Athletics) checks for chases if you want to further represent that aspect.
Cantrips are no longer unlimited. Instead spellcasters gain four cantrip slots when they first learn to cast cantrips. They gain one additional cantrip slot at character levels 4 and 10, respectively. Cantrip slots recharge after a short rest for all casters.
I personally would find this a problem: Certainly my current wizard spends over half of his combat rounds using Chill Touch. (Although almost certainly an edge case.)
I think that the issue you're having probably lies more with a specific case; (a Warlock with that particular combination of cantrip and invocation). I'd suggest addressing that problem more directly rather than an indiscriminate approach.
Simply changing the invocation so that the additional damage is based on the proficiency bonus of the warlock rather than Charisma bonus should smooth out the damage effectively.
You're unlikely to be able to burn through a stone wall with firebolt faster than you could break though it with a pick or hammer. Cantrips generally do less damage than the equivalent physical attacks: their advantage is their other effects.
You might consider the most common and effective protection against missile fire outside of being the other side of a wall: the shield. As a (Bonus action? Reaction?) allow someone proficient in a shield to apply an AC bonus equal to their (Str bonus? Proficiency bonus?) against ranged attacks (from further than 30ft? All ranged attacks?) with it. I'm suggesting a flat AC bonus rather than disadvantage to hit to allow stacking with the Dodge action.
