The top card of your library isn't in your hand, so you can't suspend it, cycle it, discard it, or activate any of its activated abilities.

You still pay all costs for that spell, including additional costs. You may also pay alternative costs.

Augur of Autumn doesn't change the times when you can play a land card from the top of your library. You can play a land only during your main phase when you have priority and the stack is empty. Doing so counts as your land play for the turn.

While you have three creatures with different powers, Augur of Autumn allows you to cast the top card of your library if it's a creature card, it's your main phase, and the stack is empty. If that creature card has flash, you'll be able to cast it any time you could cast an instant, even on an opponent's turn.

Essentially, Augur of Autumn lets you play with the top card of your library revealed only to you. Knowing what that card is becomes part of the information you have access to, just like you can look at the cards in your hand. You may look at the top card of your library whenever you want, even if you don't have priority. This action doesn't use the stack.

If the top card of your library changes during the process of casting a spell or activating an ability, you can't look at the new top card until the process of casting the spell or activating the ability ends (all targets are chosen, all costs are paid, and so on).