No, both players first place their decks on the table, then they both reveal their Leader Cards.

Rock-paper-scissors and other means of generating a random outcome are all acceptable.

Starting with the first player, you may return all 6 cards to your deck, shuffle it, draw 6 cards, and add them to your hand again, but this can only be performed once per player.

Yes, you do. You place the cards so that the top card of your deck becomes the bottom card of your life, and you must spread the cards out so that the number of cards can be seen.