disobey_gravity | Questions about bouldering

This is a really daft post, but I kind of need some gentle hand-holding.

I've been indoor climbing twice, with a partner, harness & ropes. I enjoyed it a lot, and there's one particularly tricksy looking climb I want to do--there are no holds! You're climbing inside a walled-up triangular shape and have to brace your back against the wall behind you so you can 'walk' up the wall in front! My friend could not complete it when he tried! I am DYING to try it! I am a leggy person, rather than an arm person, and it reminds me an awful lot of the way I used to climb up door frames and the like when I was a kid.

BUT that's not the point of this post.

I really want to go more regularly, but the trouble is that I can't just up and go climbing when the fancy takes me because I don't always have a partner available. I would like to go right now, but there is nobody to belay for me and due to anxiety issues, I'm not up to asking total strangers.

But! The climbing gym near me has a BOULDERING CAVE. Apart from sounding awesome, this could be the answer to my problems. Except I have this little Thing about trying new things on my own in public where people can see me. I need to plan every new expedition with military precision or it's a no-go.

So, here are some stupid questions about bouldering:

1) When you go bouldering, do you just... turn up and start climbing? I'm really used to the harness and rope combination so find the thought of going without a bit intimidating.

2) I wear glasses. Am I likely to break them if I fall? If I take them off, I won't be able to see clearly enough to plan a route in advance.

3) Are you able to do it solo, or is the gym going to turn me away for being on my bill?

4) If you are comfortable doing so, please describe your first ever bouldering experience in EXCRUCIATING step-by-step detail!

5) Does anyone else want to turn their entire house into their own private rock climbing gym? Or is that just me?