I think just like everything else every gym has their owns set of open gym rules.. Theres a gym here in our town that has no restrictions you can do anything and theres cheerleaders, tumblers and karate kids all practicing besides gymnasts. Its crazy wild. and often kids get hurt.. Most teams tell their kids not to go there for safety sake . I worked there several years and couldnt stand it.
The gym where I work at now has a team side and rec side and if you are not a team gymnasts you need to stay on your own side of the gym to avoid any accidents.. We go over rules at the beginning for all. Our team kids know they are only allowed to work on their level skils. Anything else would have to be okayed by their coach to practice on. It seems to go well and we often have other teams come to our open gym. All our welcome as long as they follow the rules
The difference between rec and open gym is coaching. Open gym is usually just show up and use the equipment on your own with coaches just supervising (and they usually have their hands full doing that!). Rec is where you are actually being coached in an organized fashion, but it is usually more emphesis on gaining skills and having fun then perfecting skills for competition.
At my gym there are certain things that only gymnasts can do, like use the high equipment for example. But it is up to the coaches who is a gymnast and who isnt. So like when I was dating a gymnast and she would "coach" me, I was allowed to do stuff that only gymnasts can do because I was being spotted and my gf actually worked there as a coach. Your best bet, ask the coaches!
It really depends on the gym. Most gyms have some rules like no going on high bar unless you have at least a level 6 skill level, no double flips unless you get the approval from a supervisor, etc. You should be able to use all the equipment and work all the skills you need. When I work open gyms I'll do a little bit of spotting and coaching if someone asks for help, but in general, I just mill around and make sure everyone's being safe.
Rec gymnastics is not the same as open gym! Rec gym is a less serious version of competitive gymnastics. Kids work out fewer hours but still have a coach and work towards learning new and harder skills everyday.
We rarely have open gym at my current gym, but one down the street has one every Friday night (from 8 to 11). You can pretty much do anything you want, but it's extremely pricy ($20). I go there occasionally with friends. It's really quite useful-when I was in Level 2 I got my back hip circle there I was so happy.
It honestly does depend on the gym. Some gyms have organized play and minimal free time, others don't care if you're doing triple backs XD