All combat styles use your STR modifier to help determine both damage and to hit chances. You can take the Weapon Finesse feat, which lists a number of styles (weapons) which will from then on use your DEX modifier to determine to hit chances, if this modifier is greater than your STR modifier. For damage, STR is still being used.
Unarmed combat is on the list, so that's Yes, No, Yes, Yes.
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