1. increase hit die to d10. d8 feels a little low for melee class with low armor.
I think we want the monk to be clearly differentiated from barbarian and fighter. Barbarian is intended to be hit (lots of HP, damage resistance). Fighter I will look at below under AC. I think monk is a light striker, so the d8 is right. I agree with you that monks are problematic, but would suggest that the problem lies elsewhere.
2. martial arts damage die increase from 1d4->1d10 to 1d6->1d12.
One way or another, they need to deal more damage. TCoE offers them a wider range of weapons, a bonus attack triggered by spending ki on anything, and a minor form of precision. For me the martial arts die increase is justified.
Other approaches I've thought of are - a 'Refocus' feature, that works like fighter action surge but gives monks a bonus action, and changing the tavern brawler and dual wielder feats to work for monks. The former by switching from granting a d4 to giving a +1 bonus to unarmed damage. The latter by adding that it obviates the use of a bonus action for the off-hand attack (might be too strong!)
3. wis mod(if positive) to ki pool.
I tried this and disliked that it kind of forced monks to prioritise wisdom. Where I landed was just - give them 2 or 3 more ki at 2nd level! Our shadow monk was fine for ki in the second half of tier 2. The painful part is being ki-starved in tier 1 and a good part of tier 2. I like other suggestions, especially the one free use approach to ki features. Monk and sorcerer have the same problem - both should probably start with more points and then scale more slowly.
4. extra skill proficiency at 1st level.
I think you make a good point here! A monk should have more skills. It feels highly appropriate, and they can make good use of them.
5. AC calculation. AC is calculated as 10 + two modifiers from STR, DEX, CON or WIS.
This would give more room for diverse types of monks and still keep their starting AC at 15/16.
Where barbarians take a punch, fighters deflect them with high AC. Meaning I think monk
shouldn't have better AC than they do now. They have the tools to play as a kiting class - movement, bonus action dodge or disengage - they just need the ki to do so.
Would all 5 changes be too much or monk is so bad that it might need more than these 5 simple fixes?
Were I picking from your suggestions (and tweaking) it would be - increase martial arts die, give monks a flat 2 extra ki at level 2, extra skill proficiency. Those three changes would all feel meaningful and make them more fun to play.