This sounds like a lot of fun! The adjustments suggested in this thread would make it a lot better.
Adjusting according to weapon usage would actually differentiate weapons from each other and give purpose to having different tools at hand, something that I've always thought very odd to be lacking.
I think the issues of duration are weird. I think things should be left as they are now: they last as written, with a new round starting for a character at the beginning of each of that character's turns.
The dice you roll should match:
Melee: the base damage of your weapon
Ranged: base damage increased by one die for ammunition weapons (non-rolling weapons like the blowgun can be raised to the nearest die roll with an average greater than the fixed damage number, 1d2 in this case)
Spells: based on max spell slot level:
- 0: 1
- 1: d2
- 2: d4
- 3: d6
- 4: d8
- 5: d10
- 6: d12
- 7: d4+d10
- 8: d6+d10
- 9: d8+d10
Bonus Action: d4 or one die less than it would have been as an action, whichever is lower
Disengage, Dodge: 0
Dash: d2
Help: d4
Movement, Hide, Use an Object: d6
Search: d10
Ready: on your turn, you can Ready any actions, movement, etc, for which you rolled initiative
Gained Options: If a choice on your turn grants you additional options for which you have not rolled, you may use them, but you take a d4 penalty for each on your initiative roll for the next round
You could add consequences, too. For example, if you get hit, you could have to add the dice for the attack you were hit by to your initiative for the next round. E.g. If you get hit by a dagger, you have to add a d4; if a longbow, a d10; if a 7th level spell, a d4+d10.
On the other hand, if you gained HP or THP, you could decrease your initiative by a d6, or if hit that round, cancel all additions from hits.
Edit:
I like @
Athinar's idea below about a cost to talking. I'd say you can say up to 20 words if you can be heard. If you say anymore, you roll an additional d20. (I think a d100 would be too steep.)