The player who holds the 2 of clubs must lead it to the first trick.
Yes. If you have a card of the suit that was led, you must play one. If you have none, you may play any card.
You may not lead a heart until a heart has been played on an earlier trick. That moment, usually when someone discards a heart on another suit, is called breaking hearts. If your hand is only hearts, you may lead one anyway.
No. There is no trump: the highest card of the suit that was led wins the trick, and the winner leads the next one.
In the standard rules, yes. Some groups ban it unless you hold only penalty cards, so agree before you start.