MTG: Azorius Chancery on first turn?

Well, you can play it first turn. But it's no freebie.

The order is:

Azorius Chancery comes into play tapped.

Azorius Chancery's ability (return a land you control to your hand) goes on the stack.

Azorius Chancery's ability resolves, meaning you return a land you control to your hand. The only valid target is Azorius Chancery, therefore Azorius Chancery returns to your hand.

It's definitely not a freebie. Since it doesn't say "Another land", the card itself is a legal choice for the return to hand effect.

That's not to say there isn't a way to potentially make use of it first turn, though it likely slows you down in the long run. For example, if you were to first play Lotus Petal and sac it to play Amulet of Vigor, you could then untap the Chancery and then tap it for the 2 mana before returning it to your hand. Slows your mana base down for future turns, but viable and gives an example of how it might be useful.

No, you would still return a land to hand, but it would be the Chancery. When you play the land the return to hand ability goes on the stack, and since you would have nothing else in play, you would have to bounce your Chancery.

It's a very bad play, since you do have to follow the instructions.

That means it WILL bounce itself.