Not sure if umpire age is a major factor but; it did come into play with us this weekend.
It's a factor in that a younger umpire will usually be a less experienced umpire. I work with and train young umpires for a local league and there are some good ones out there. But nothing can replace the experience of actually working games. Ideally, you would like to have them get a few seasons of lower-level rec league ball under their belts before turning them loose in travel ball tournaments. I know that when I first started out it took a couple of seasons to get comfortable with positioning and mechanics, as well as dealing with coaches and handling unusual plays or situations.
On your specific plays:
1) Assuming no issue with interference and the three foot running lane, in which case the batter-runner would be out, when a defensive player not involved in the game touches a live ball it is considered a blocked ball. It doesn't matter if the ball would have rolled into the dugout or not. The ball is dead and the runners are awarded two bases from their position at the time the throw was made.
2) It doesn't matter if the coach "tried" to get out of the way, or if he "accidently" interfered. If the umpire judges that the coach's positioning or movement prevented the fielder from making the catch then the batter is out. The ball is dead and any other runners are returned to the bases held at the time of the pitch. Simply, the fielder has the right of way and is entitled to an unimpeded opportunity to make the play. The coach may move any distance and any direction anywhere on the field to give the fielder room. If he doesn't, or picks the wrong direction, that's his bad.
3) An initial play at first base is always the base umpire's responsibility. The plate umpire's first duty is to watch the lead runners, so I'm not surprised that the plate umpire didn't make this call. It's not his to make.
That the ball touched the ground doesn't automatically make the runner safe. The catch of a thrown ball has a different definition and standard than the catch of a batted fly ball. If the fielder had her glove around the ball and was able to lift it from the ground, without adjusting or bobbling the ball, then she has demonstrated control of the ball. This can still be a valid catch and tag of the base for an out.
4) once a batted ball is touched or deflected by a fielder, any interference with a subsequent fielder trying to get the deflected ball must be intentional. If the runner did not intentionally run into the fielder, then there is no rule violation. Live ball, play on.
When a runner does interfere, it is the runner who is out, not the batter.