Good question. It seems there are a few parts to it. Hopefully I'll be able to address at least a few.
With regards to contacting a GM about random or impromtu events, the best way to do that is by contacting the GM directly. That can be done in-game, as you mentioned. But if an idea or question comes to you when the GM isn't available in game, a Private Message here on the forums is a good choice. Some GMs have even more options to contact them, through email or a chat program. Take a look at the specific GM's profile and see what options are available. All GMs are open to, in fact most of us crave, those sorts of inquiries and requests.
At times reading your post I thought you might be asking about how to identify a GM who orchestrates an impromptu event. This is important, of course, because if you don't know who the GM is, it's impossible to follow up on anything. In those circumstances I think the best approach is to post an inquiry on the forums. Just breifly describe the event and ask who was involved so that you may contact the GM with some follow up questions and/or ideas. As I said above, all our GMs are open to these kinds of ideas and questions, and so whoever the GM was will likely get back to you relatively quickly.
I hope some of the statements above address your questions. Thanks for asking them. Be well.
Rhizome
