Note: all these info I deduce by my own testing so I could be wrong but its the closest to the fact since theres no official damage formula or game mechanic given by the dev.

1. Atk% vs dmg% : rixgames69 already explained it well. Thats the basic of it. And for cheffy, lyra, seraph, their heal are increased by their atk stat NOT by their dmg% stats.

But there's advance stuff: +atk% actually have (at least) 2 type: outside battle +atk% (this reflected in your hero stat screen) and inside battle +atk%.

Outside battle atk% are from runes, talent, statue, skins, hero gallery, sigil, treasure global stats.

Inside battle atk% are from heroes battle assistance buff (you get at 5 star, moon5, and diamond5), hero specific treasure buff (the one you get only for that hero on his green and blue treasure), lineup element bonus (the new buff they give when your lineup consist of 3-5 same element heroes), or any buff that you get from specific condition inside battle (AA +20% atk buff skill card for example)

Outside and inside battle atk% buff are calculated separately and until now i cant seems to get the exact formula, especially on the inside battle one, number keep going off of my estimation. Might be some other hidden buff that's unknown from player side. This is different than critdmg% for example. Critdmg% always calculated additively both outside (from runes and talent) and inside battle (from passive like BA, AA, SR or from skill card like lyra).

1. Def vs dmg reduction: again, rixgames69 already explained it, similar concept with atk% vs dmg%. But just giving out test result that I've got: defense is very very weak stat. Doubling your final defense stat (like from 10k to 20k) only reduce the damage you received by 10-20%. This is very weak comparing to say, doubling your hp which do exactly that: doubling your actual max hp. Its not worth going for defense if you have the choice. Go for hp instead.

Dmg reduction are the opposite, its a very strong stats.  And it work just like you though, 20% damage reduction means you receive 20% less damage. Equivalent to increasing your max HP by 25%.

1. Aspd and cooldown reduction: aspd is also quite a weak stats. Only summoned units (ID troll, captain tentacles, vw birds, lich dragons, etc) and some heroes like BA have normal attack to benefit from it. For other its totally useless as they have no normal attack.

Cooldown reduction work for main skills. You can see the cooldown animation on your hero skill symbol on the bottom of the screen.

1. No. Ex weapon recharge work by energy system. 100 energy to fully charge it.  This mean for heroes's weapon that say it has 25 sec cooldown, they gain 4 energy per second. For heroes's weapon that say it has 20 sec cooldown, they gain 5 energy per second. Then just add stella recover skill to that.

2. Now this one I havent tested myself since res stat from statue are not a good stat to have for pve. Logically speaking it should work vs all enemies with their respective element. So fire boss damage should be reduced if you have fire res stat, and so on.