Ball hit down 3rd baseline. F5 throws wide right of first base. First baseman comes off base to catch the errant throw, runner runs through the glove and the ball pops out. Who gets the error?

E5.

How about ball hit to 3B, his throw bounces, but is (what I think) to be a catchable ball and 1B misses it. Is that a throwing error on 3B due to the bounce, or a fielding error on 1B?

E5 still.

E5 since he should have made the throw.

It should almost always be on the person who made the errant throw because it's with ordinary effort that the throw needs to be made, unless it's a real good throw right at the 1B's chest it should prolly be an E5, E6, E4, E1 or E2 unless the 1B makes an errant throw somewhere else then that's an E3.