Yes, it's typical. Think about it...the same competitive spirit which gets one into a nursing program is the same competitive spirit which will get one through a nursing program. It's an ingrained trait...it's a part of you (and your classmates). I'm just finishing my 3rd semester of an ADN program, and it's always been an underlying theme.
I used to throw around the word "clique" as negative, but I realize I do have my own "clique", too...I prefer to refer to us as just a group who bonded early in the program and rely on each other heavily for emotional and intellectual support. There's nothing wrong with that. Of course, there are those who just didn't seem to hit it off with others at the beginning, and they tend to feel isolated. That's really sad, because we all NEED a few others with whom to relate. It sounds like you're just getting started, though, so embrace a clique of your own, or you'll go crazy.
Now, on to people being rude and gossiping...that, my friend, is probably from the female element of nursing. I am a proud female, but I'm also a realistic female. We tend to just be that way. I used to work in HR at a large bank. The banking industry is dominated by females, and the same type of things happened there. I can't tell you the number of times I had to hold a poor teller's hand and listen to her cry because "so and so" didn't say "hello" to her that morning. We are female, we are emotional, we are delicate, but we can also be royal "you know what's", too.
All I can say is this is a very stressful time for all of you. There are going to be heartaches, there are going to be hurt feelings, there is going to be drama. There is no way to avoid it or stop it. But, you just keep your head up, and you will be able to rise above it all. And, believe me, one day you will laugh about all the silliness you are experiencing...and your classmates will, too! Good luck, hold on, and just enjoy the ride!!!!! It will actually go by much faster than you think!