Me my Girlfriend and her Cat?

Basically my girlfriend ’s cat has been a big issue for me and it is driving me crazy: I am based in here in the USA but I am African by birth and I grew up in a society where cats are seen as a demonic symbol or a sign of evil also most people from Africa will tell you they don’t like cats, but I really don’t care about that. I love my girlfriend when I met her and she told me she had a cat and she said she grew up liking cats, i told her no worries that I am okay with cats because I am a open minded person and I also don’t believe cats are actually demonic and also do not believe in superstition, and I also make her understand I am not use to cats but I will try and get use to it cuz I love her.

5 months into our relationship and we moved in together, this is what the cat has been doing.

Cat poop on the carpet/rug everyday (she doesn’t use her poop cage)

Cat poop stinks and smell so bad.

Cat always sleeps on the bed and make so much noise also scratches the duvet.

Cat also always just jump on the bed and wake me up.

Cat sneezes all the time while sleeping on my girlfriend in the room.

Cat vomits white foams and sometimes blood.

When I am eating the cat keeps staring at me and keeps meowing or screaming.

My girlfriend doesn’t want to do anything about this cat and it is driving me nuts, one time I asked her we should lock the room door when we wanna sleep she said okay but when hears the cat scratching the door she will get up in the night and open the room door.

My girlfriend use the spoon we use in eating to dish the cats food and also use the spoon to trash the cat eating tray after the cat is done eating.

She doesn’t wash her hands after touching the cat all day.

Anytime we wanna have sex in the night the cat comes in the bed and girlfriend doesn’t care but it is a turnoff for me.

The cat sleep on my girlfriends chest most night I can’t even cuddle her cuz she will think I am pushing the cat away.

What should I do?