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first of read this it explains the stack and more importantly priority

Your knowledge of the stack seems to be ok but the terminology you use is confusing.

>>Giant Growth > Dismember, correct?

correct. the stack resolves in reversed order. Last in First out

1) Yes. In order to cast a spell you need a legal target. Lets say you want to cast Fork, this means you need to cast it in response to someone casting a spell and passing you priority, before the stack resolves. Because it needs to copy a spell on the stack. Once a spell resolves it's no longer a spell. Spells only exist on the stack. Cards in play are called permanents and not spells and everything else goes by the name card.

2) Tapping something for some effect like mana production is called an activated ability. Activated abilities can be used at instant speed unless the description says otherwise. Interrupt speed doesn't exist anymore, everything that uses the stack is played at either instant or sorcery speed.
You can tap llanowar elves and add mana to your mana pool when you have priority, you can use this mana to play giant growth. So your information is incorrect. Do know that you can't tap llanowar elves the turn it came into play because of summoning sickness. Also know that you need priority in order to do something even if what you are doing works at instant speed.