Each player chooses to draw any number of cards from zero to seven. First the player whose turn it is chooses how many cards to draw, then draws those cards, then each other player in turn order does the same.

The exiled cards are exiled face up. You’ll see them before you choose how many cards to draw.

Diminishing Returns won’t be put into your graveyard until after it’s finished resolving, which means it won’t be shuffled into your library as part of its own effect.