Q1 - Yes, that's legal. There must be team control before a backcourt violation can be called.
Q2 - Yes, there is a "carry" call. You're correct in that this is technically a travel or double dribble (because the dribble ends when the ball is palmed), however, if you called a double dribble when the player clearly didn't stop his dribbling attempt, you'd get quite a few odd looks.