Searching through someone's Internet history is not good. Not only is it an invasion of privacy, but it's possible to get all kinds of impressions that may not be true. Depending on the day, I hate to think what weird impressions people could get about me by looking through my Internet history. I tend to end up a lot of weird places on the Internet. Personally I wouldn't stand for being in a relationship with someone who was "constantly checking [my] phone" or looking up my Internet history and I would never do that to her either.

I don't know the context of his contact with other women, so I can't say whether or not that's cause for concern. If they are just friends (he doesn't do anything romantic/sexual with them and doesn't try to) then I don't see any reason for concern there.