Is using a chat an appropriate way to troubleshoot a problem with
someone from the main site?
Sure. It would still be nice to add back new information (discovered in chat) to the question, so that there isn't a huge disconnect between the question-as-asked an the answer finally obtained.
- Should I just rename my chat room to "Troubleshooting" to allow others to use it for future questions?
- How can we get the user's attention to let them know that we are trying to chat with them?
If there are too many comments on a post, the system automatically suggests creating a chatroom. When it does so, relevant comments are added to automatically added to the chatroom as chat messages. The room is also named something like "Discussion (on XYZ|between X and Y)". A comment is left on the original post along the lines of:
Let us [continue this discussion in chat](link-to-chatroom). You can see many such rooms with, for example, Ask Ubuntu.
This, IMO, is the best way of starting a chat about a post. It preserves history, the comment ensures both a notification to the OP, and provides a way for others to find where the discussion continued.
I'm not sure why it didn't trigger here. Probably a bug.
It is not currently possible for normal users to create such a chatroom (with automatic comment import) before the message appears. However, mods can, and, IIRC, they can also invite a user without sufficient rep to specific rooms. So, you can flag for moderator attention and ask for the discussion to be moved to chat.
If you don't want that, then you'll have to manually create a room, and if the user doesn't have a chat account, comment under their post asking them to come there. If they already have a chat account, you can create a room and invite users there.
Is there a way to delete my chat room that I don't know about?
Become a mod? ;)