Would there be any chance for me (a junior in high school) to get some sort of stage manager/production internship where I would be able to go after school to evening performances and get to observe them? Has anyone had success in doing so? I really would love to do this for any Broadway or Off-Broadway show or cabaret venues like 54 Below, etc., and was wondering what the chances would be if I wrote to them and asked? Help would be greatly appreciated.
I think the best place to look for a stage manager internship is the official portal: Stage Managers > tagged internship programs >> https://www.stagemanagers.org/tag/internship-programs/ There're also conferences and symposia for students.
I believe that due to union agreements, it would be practically impossible to intern on Broadway in stage management. However, there might be opportunities in the producer's office or even company management.
^That's not true. There are many Broadway stage management PAs and they aren't union.
To the OP, it sounds like you want shadowing opportunities which would be "easier" to obtain, rather than full on internships - especially at your age and skill level. Contact PSMs or PMs directly with requests.