Is it normal i want to end our friendship?

But I want to do it nicely!
I have been really good friends with a girl for about two years now but for the whole two years, it's been a bit of a drag. I'll try sum it up and keep it short.
-I have moved away to university. She still lives at home. Finding it hard to keep in touch and I'm trying my best to settle into university so I don't have much time for her. Well the amount of time she would like from me.
-She is extremely negative and cynical. She makes me feel really down when I am with her.
-She talks about her family dying all the time. Especially her Grandmas death. I know it's okay to talk about it but it happened ten years ago. Three of my grandparents all died ten years ago and I don't feel the need to talk about it. She wants to talk about death EVERYTIME we talk, which used to be every day. I just do not want to talk about death!
-Her whole family suffers from serious mental illnesses. She talks about that every time we talk. The same story over and over again. My mum used to suffer from a mental illness which I had to put up with when I was a young child, alone. My mum was a single mum. Her mum had the help of their whole family. Mine had no help whatsoever. But I still don't feel the need to talk about it every single day, if at all.
-I really enjoyed being around her family until recently. Out of nowhere, he brother sent me a load of disgusting, highly sexual messages over facebook. Now the whole family act funny with me. I didn't return any of the messages. I just told him to go away. He has done it to many other girls too.
-Six months into our friendship she told me she was a lesbian. Whenever she gets drunk, she texts me saying she likes someone (never mentions this whilst sober) and says I am not allowed to know. I was once talking about a guy I liked, who had a girlfriend, and she replied well we all want someone we can't have.
-She constantly brings down my boyfriend. Okay, he isn't perfect but I am not exactly innocent either. But she thinks I am an absolute angel and he is the devil possessed. Our relationship is good. And whenever it goes wrong, half the time it's my fault. I am not an angel.
-A while a go she blasted me for having a few one night stands. Apparently I have no respect for myself. Men only want to use women. But I was using the men too! We were both using each other for a bit of fun. I didn't sleep around excessively, it was only a few times.

Just being around her makes me depressed. She doesn't really make me laugh or make me feel good. She sucks all positivity out of everything and she thinks no one can be trusted, everyone is out to get you and is obsessed with death, mental disease and other negative things. I am not too good at the moment, and I feel I cannot have her bringing me down even more. Is it normal I do not want a friendship with her?