He sure doesn't sound like a one-woman man. I think his constant contact with other woman would bother just about any girlfriend.

I'm not into texting, myself, so I find the amount of time that some people spend on it amazing. I think it's rude to engage in texting during what should be together time with a significant other. I believe you would have a right to ask him to not be constantly interacting with his phone when the two of you are alone together. I would find that intolerable.

Try and learn what ended his two marriages. If it was getting involved with other women, then I wouldn't have high hopes for him being faithful.