A few of the things that your girlfriend is doing seem excessive, but people on this thread are jumping the gun a bit. I don't think it's that strange tbh.
I had a similar thing with my girlfriend when we first got together. I continued to hang out with my female friends, sometimes just as a two, which looking back is a no no early on in a relationship before you've come to fully trust and understand each other. I totally get why my girlfriend felt weird about it.
My girlfriend is also from another country, where I was living when we got together, and to be fair to her she wasn't lying when she said that it isn't normal for guys and girls who aren't dating to hang out. After I got together with my girlfriend, two of my female friends (one of which i'd known for over a year) refused to meet me anymore. They said that it would feel weird and that they'd feel sorry for my girlfriend. I haven't spoken to either of them since. Strange huh.
In my girlfriend's defense, she never told me that I couldn't have female friends, she just got kinda weird about it which sometimes caused arguments (which are a real ball ache in your second language!). We don't argue about it anymore. I'm upfront with who i'm meeting, as is she, and we've been together long enough to trust each other.
Does your girlfriend have any reason not to trust you? Something you've done? Or is your relationship still young? If you like her, give her the benefit of the doubt and talk to her about it. If she is just crazy and possessive, then i'm sure the relationship won't last long anyway before one of you snaps.