AG#1 your questions with answers per rules from ASA, USSSA, and SSUSA below
AG#1 original post - runners on 1st and 2nd no outs, batter hits a ball up the middle which goes off the pitchers glove and then hits the runner who was advancing to 3rd,
1) is the runner out? Yes in all three associations, ASA Rule 8, Section 1, para E. ; USSSA Rule 8, Section 2, para 1 also addressed in Rule 9, Section 2, para K ; SSUSA Rule 8.2.C.2 and also Rule 9.1.X
2) does this remain a live ball play on? Yes the ball is alive in all three associations until it strikes the runner then the runner is out and dead ball. If the ball were not to strike a runner it remains alive for the defense to make a play, etc, etc
3) is the call also determined on if a defensive player had an opportunity to make a play? defensive player position is considered, if ball has passed defensive players and strikes runner, no effect, if strikes runner prior to and in front of defensive player, runner is always out
4) would the call be different it the ball went off the pitchers leg instead of his glove? NO in all three associations, ball is alive regardless of hitting glove, player part, or uniform
Answers above from NCASAUmp are incorrect for 1,2,3 and correct for 4
Answers from EAJuggalo are incorrect