Can you use activated abilities of creatures the turn they ETB if they do not tap the creature?
As long as you have what is required to activate the ability, absolutely.
RESOLVED
But if activation cost asks you to tap creature to activate, Then you cannot cast it on the turn that it comes into play unless it has haste.
Yes. Correct.
Orrrr if the activation cost is "tap a creature you control : get such and such effect"
You could tap a creature with summoning sickness to pay this cost, correct?
Yes. If a creature with summoning sickness has an ability with the {T} symbol, you can't use it. Everything else is fair game.