1. His cheating (what's the reason for it)
can you tell us more about this? youre saying he cheated, right? how long ago was this, and is it ongoing?
2. When he brings up his family problems (but is scared to talk about how to solve it after complains about is)
more than likely, he just wants to talk, to vent. just listen. if hes not asking for advice, dont give it.
3. His lying (why is he doing it when he already know i know the truth but he'll still go fully through with it then when confronted he gets quiet)
what kind of lying, and about what?
the thing about lying is that the person doing it is already avoiding the truth. trying to press them further wont tend to get you anywhere but frustrated.
4. He would stir up a fight out of know where. LIKE COMPLETELY OUT OF THE BLUE "bipolar mood" be extremely rude after a good laughing moment between us. Then i ask what was that for. then he'll respond with " i dont wanna talk about it" , "hows was your day","what are you eating" or say whats happens in a movie thats he watching. Like the switches that he makes wont even match whats happening at the moment.
without more to go on, i suspect he realizes what he said was uncalled for and out of place, and wants to move past it. how do you feel about that?