If I'm billing hourly and I'm billing an 8 hour day, I'm including a 30 minute lunch, regardless of rate. Anything longer than that is off the clock. If I'm billing 4 hours, then sure, no lunch. This is only true if I have a single client project on the go; if I'm billing piecemeal through the day (which I never want to do) then yes I'm eating on my own time.
I get being hesitant to bill for certain kinds of troubleshooting, but I think it comes down a lot to what the scope of the project is. If I'm on something that is multiple weeks of work, and I'm dealing with a problem that I would be encountering and would be expected to solve if I were working full-time, then it's billable.