No, not unless he's deemed to have intentionally interfered with the ball.
The fielder made a decision to throw the batter out at first instead of throwing the runner out at home. This is considered a fielders choice.
It isn't a hit. It is a fielders choice.
To get a force out when a runner is on 1st base and the ball is hit, you can throw the ball to 2nd base.
No. This would be a fielders choice and would not count as a hit for the batter.
Error on the throw
For the play you describe, it would be a hit. A fielder's choice is when a fielder chooses to throw to another base instead of 1st base to retire the batter. I doubt the center fielder had a chance to throw out the batter at 1st base.
Right fielders ordinarily have better arms because they are in the farthest position from 3rd base. If a ball is hit far out to left field, the runner is often let have 1st base. Right fielders need a rocket of an arm in order to stop the runner from getting on 3rd base, or rounding 3rd to home
The first baseman has a lot of responsibilities. They have to catch all the balls that their fielders throw to get runners out. They have to field all the bad throw of their fielders. They have to act as the cutoff player when a ball hit to the outfield comes home. They are responsible for fielding bunts and throwing girls out at first.
No hit it is a fielders choice
A fielder's choice is when a fielder has choosen to make an out on another runner on base when he could of gotten the batter/runner out instead. The batter/runner is safe, therefore reaching base via a fielder's choice. Please note that this counts as an at-bat and goes against the batter's batting average.
Yes, the play ends, the batter is awarded first base, and the runner that was hit is automatically out.
Generally speaking, it would be a hit unless the fielder clearly had enough time to throw out the runner and did some other action instead (such as an attempt to tag a base runner, but not throw the ball).