Yes, you should be very worried.... about your judgment in general. Dating someone 14 years your elder - though I don't know your actual ages- is somewhat suspect (of your own best judgment). Dating a man who is not actually single is suspect (of your own best judgment). Dating a man who'd going through a prolonged/twisting/never-ending divorce is suspect (of your own best judgment). Dating someone and being preoccupied with their cell phone usage is suspect (of your own best judgment).
You see what I'm getting at? The situation itself is rather rotten and worrisome. You are asking me if I think your still married boyfriend is up to shady business. Read that sentence again and answer it. I don't want to say it is categorically doomed, but think hard of how you are actively contributing to a shaky lifestyle right now. I'd give yourself some very clear timelines and markers with which to proceed the next few weeks and months. If things are still worrisome - time to not be "that woman."
Do the fade away....
You are asking me if I think your still married boyfriend is up to shady business.-This! (The answer is yes btw.)