Wrong forum to ask on really, we have a bunch of idiots that are going to say stupid things, try to ignore them unless you want this locked.
You need to trust her for a start, i'm sure you have girls as friends if you're just friends with them, why couldn't she be the same?
As for being close, then get closer to her. Take an interest in her hobbys, interests. Open up to her, tell her how you're feeling..it can't be one way, if you want her to share her feelinsg with you then you should do the same back, even if it is a bad thing..hiding it away will only cause your relationship to break down.
Like most problems in relationships, it all comes down to talking to them, gotta have good communication skills with them.
Asking her if anythings going on with the other guy is only showing you don't trust her, have some faith in her and make an effort to be with her and do things she likes, make an effort to get to know her better.