unless your in an area of the world where its normal for a woman to call a male friend "baby" she's cheating on you.
my personal preference in all of this is pretty simple. i wouldn't bother confronting her. or having discussions with her about it. etc.
a liar is a liar and i've learned over time that even when you confront them they will only reveal what they know they have to. even if she comes out and admits this or that, there's probably still lots more that you don't even know about.
so i would just get to walking.
if you live together arrange for another place where you can live until you get your own place. don't tell her nothing. one day take the day off work, move all yoru stuff, and when she gets back just say "im moving out. i'll cover the rent for one month, then you're on your own."
move on and never ever look back.
some on here will say im being overly harsh. that you shoudl hear her out and give her a chance.
based on what you've written that doesn't seem necessary to me. all the red flags are there.
all i can say is that confronting liars with the expectation that they will come clean almost never works. liars will lie until their absolute last breath. it's just not worth the head ache.
its tough when you've put 2 years into something only to get cheated on, but try to look at the positive - THANK GOD she did it now and not 15 years down the road.
i would also put forward that she might blind side you very soon. she's being sloppy, and that's usually intentional. she's giving you a heads up that the sh*t is about to hit the fan, this way she doesnt feel so guilty one day ripping your heart out.
go with your gut and your intuition. sounds to me like you know how this situation is going to end. do a pre-emptive strike and move on.