Boyfriend cheated several times, we decided to not live together, we r still together. He has a new  female best friend.Should I be worried?

Say he cheats with her, are you actually going to break up or will you forgive him like all the other times? If you won't leave him then whether or not he cheats doesn't matter. I think you should cut to the chase and negotiate an open relationship. At least this way you will be able to keep your options open too.

If you really think this female is his best friend, then I have some swamp land in Florida to see you.  He's a serial cheater, of course you should be "worried."

When someone shows you that you can't trust them, believe them.

You are a mug staying with this loser. Dump him and find a worthwhile partner. He's a player and will never change.

So your boyfriend cheated multiple times but instead of breaking up, you decided to not live together allowing him to easily cheat on you more? 

Once a cheat, always a cheat. Dump his @ss

Yes if yall are still together and just moved away from each other you should