Scandinavian Defense (Black)

No. You can check 3...Qe5+ and then play 4...c6 to retreat 5...Qc7, but 3...Qa5, 3...Qd6 and 3...Qd8 are better.

White has more center control and c7 is a target. Maybe not more then +0.5 because the queens are off the board?

White has more center control and c7 is a target. Maybe not more then +0.5 because the queens are off the board?
It's not logical to block the check like that: White will win more time by attacking the Black Queen again with d4, or Nf3 if he blocks with the bishop.