My bf like to play online on his PS3 which is fine. What I do not like is the messaging chatroom thing. I didn't have any worries until one time i logged on to play ad I saw these weird messages from a girl, tey were messaging back and forth a few times and it was kind of hurtful. It took some time for him to prove to me and change. He said that it was nothing and nothing would have came from it because she was fom Europe. Even though we were only together for a month at that time.. I think that's cheating. Is that normal? When I confronted him about it calmly, he was speechless and when I asked what was that all about he lied the first time and then the second time I asked he said it was nothing, nothing would came from it. Why would he lie about or do that?

As for some messaging back and forth with someone on another continent? I wouldn't worry about that too much...also, as you said, you just got together.
Your feelings are understandable, but often, people just want the reassurance that they "could", that they "have what it takes". Especially people in a relationship often end up wondering about their perceived "value" to others. Their partner loves them crazy, but are they also still attractive and charming to people outside of the relation?
This "probing" can quickly turn into light flirting, and, possibly, more. Most likely he merely enjoyed some sexting with a (probably) girl on another continent, without giving much thought to it but satisfied with himself that he "got there", never intending for it to be more than that.
Now, he may be one to look out for if he's out with the buddies and takes calls in another room, but unless there's specific reasons to doubt it, i'd just write it off as a stupid "manly prowess" type of thing. Yeah, they need to prove it to themselves. Not much better than us dressing up for the night out and feeling good if someone tries to chat us up, but they tend to take it further.
Also, as shade said: the amount of commitment usually becomes higher the longer you are in a relation-
He shouldn't be doing that kind of thing while in a relationship.
He got mad when you told him to imagine you doing it with another guy, so why the fuck is he doing it to you?
And one thing to consider, there's probably a lot more commitment between the two of you now than there is one month in.
I think that girl who's talking to your boyfriend is just a scam. I may be wrong but it happens a lot. Even if it could be a scam, he should have told her to stop talking to him that way.