Tiger claw will deal damage with both claws ONLY if you use Dragon claw as finisher
Fools mod on mainhand is for whirlwind as you get more hit checks,
as for Dragon claw or standard claw hits each weapon checks individually meaning if you need AR you run 2x fools or angelics
Deadly strike, ed (to the weapon itself) psn% and all other modifiers will function on the off hand but only when the off hand strikes, it won't carry the effects to the main hand