Yes if a runner doesn't touch home plate and enters the dugout an Umpire can call him out the second he leaves the dirt surrounding the area of the home plate and the two batter's boxes however Major League Umpires may not opt to declare a runner out even if he missed home plate unless the opposing team appeals the call or tags the runner.
No, if the fielder is out of the field of play (in the stands), then the batter is not out.
Maybe in High School or Little League. Usually not.
it depends on the umpire but usually yes
yes. No one including the basepath coaches are allowed to touch a base runner prior to touching home plate
No. To force an out, the defensive player has to touch the runner with the ball or touch the runner with the glove while the ball is in the glove. A thrown ball touching a runner does not count.
If it is a force (i.e. there are people on all the bases behind the runner) play, then yes, the baseman needs to touch the base to get the runner out. If the runner is not required to move to that base, then the baseman must tag the runner to get him out. The baseman does not NEED to touch the base to record the out. The defense may tag the runner OR the bag.
Yes. The runner must touch home plate prior to being tagged for the run to score. If the defensive team does not tag the runner or step on home plate, the run counts. This is an appeal play. If no appeal is made by the defensive team. the run counts.
On a Home Run, the runner is still required to touch all bases, even if he is entitled a run. If he misses any base, including Home Plate, and makes no attempt to return to the base to touch it, he will be declared Out and his run does not score. If other runners are also running and touch all of the bases, their runs will score. If there are two outs with runners on, only the runners who crossed the plate before his run would score.