Team A is on offense. A1 is bringing up the ball a fould is called on A2 off the ball. Team B is in the Bonus. Team B gets to shoot the 1 and 1 right becuase it is not a player control fould.

Also does handchecking by the player dribbling the ball constitute as player control foul?

Yes, Team B gets the shoot the one and one. As far as hand checking by the offensive player, I have never seen that. But, if the offensive player displaces the defensive player that has a legal gaurding position, Tweet, we are going the other way.

FED - correct, shoot the 1-and-1
NCAA -- incorrect, team control foul. No FTs

Although I'm having a hard time visualizing handchecking by the dribbler, any common foul by the player in control of the ball is a player control foul. No FTs to the offended team.