Whew this is a lot of questions all in one.
First off, yes I have been to bath houses many times. In the end, they aren't quite my thing. That's not a judgmental statement as I do still occasionally go - maybe like once or twice a year. For me, I like sex to brew naturally - either from sexual tension with a friend or spontaneously and unexpected. To me, going to bath houses or hook up off apps often times feels forced. It also feels like I am on a mission and if that mission fails then I am SUPER disappointed.
Most people in bath houses tend to go to private rooms rather than play out in the open. But if they do play in the open, you can certainly watch. I just recommend not trying to join in unless given an obvious signal to do so. I have a bit of an exhibitionist side (shocker, I know) and I enjoy it when people watch. But when they just decide to reach a hand in there without my consent, it's very frustrating.
So know that if you decide to go just have fun solo with yourself, at some point, someone may feel like it is an invitation when it really isn't. Therefore it is a good idea to have something in mind - a blanket statement - that you can say if they try to randomly join in your fun.
As for my first experience with a guy, well that is an incredibly long story that I don't have time to tell here. Also, I kind of would like to save it for a book chapter down the road. This isn't me avoiding transparency. It just isn't the right time or space for it. But I will say that it was a spontaneous brief encounter in a public place and it was a wonderful experience for me. I didn't know the guy and I never saw him again. But I will always be grateful to him for providing my first experience which helped me ensure my attraction to men.
When it comes to your being a virgin, don't do anything if you aren't sure about it. When having sex, your hormones change dramatically after it's done. This post hormonal shift can contribute to feelings like guilt. So chances are, if you weren't sure to begin with, chances are you might regret it being your first experience afterwards.
My best recommendation is to NOT do a hookup over the apps as your first experience. App hookups are weird. Like I said above, it can easily feel forced which, to me, isn't as fun if it comes naturally. And frequently the person you meet isn't quite how you imagined them from the profile. That can make the energy wonky too.
If you are using the apps, then use them to make a new friend - someone you can feel comfortable with and take it slow with and enjoy silly moments. I don't think it necessarily means it has to be a boyfriend. But let it be someone you appreciate and who appreciates you back. My first time being a spontaneous adventure isn't the right route for everyone. Based on how you phrased everything in your question, doing it this other way sounds like the right speed for you.