No, he could throw to home plate!
The runner is safe at third and the runner is safe at first.
another player
Yes, but he must first make a bluff to a runner on third--then bluff or throw to first.
yes
If the pitcher is in the pitching circle and the runner doesn't commit either to advance or return the runner is out. So long as the pitcher doesn't make any attempt to throw the ball and get the runner out.
The runner is probably out for interference by running into a fielder, if not, he is out if the throw to first beat the runner and the first baseman, or whom ever is covering first, had his foot on the bag when he received the ball.
The runner is out unless they are on the bag in time .If the runner is in foul territory, it is just counted as foul.
Most likely it is neither a hit nor an error. In most cases this would be scored a "Fielder's Choice". It could be a hit if, in the scorers judgement, the batter would have beat the throw to first had the pitcher not hesitated to hold the runner. It would not be an error unless the pitcher bobbled or misplayed the ball. To clarify, a "Fielder's Choice" can be recorded even if an out is not registered.
That would depend on the play. If there are men on first and third and no outs and the batter hits a fly ball that looks like it could be a sacrifice fly, the pitcher will back up home because he will expect the outfielder to throw the ball to home plate after making the catch. If there are men on first and third and the batter hits a single to right field, the pitcher will back up third base just in case the runner on first tries for third and the right fielder makes a poor throw.
The runner isn't awarded anything. If the fielder can get the ball in time, the runner can still be thrown out at second. The runner is only awarded if the ball is thrown out of the playing field, such as the dugout or the stands. It is then declared a dead ball and is treated like a ground-rule double; The runner receives his extra base.
you could check the runners at 2nd and 3rd, and then throw to first base. Once that is done, throw it home to prevent the runner on 3rd to go home.
The out to third is more risky, and you might end up with two men on vs an easy out.