They are both wrong. Especially the first one which is riddled with errors. I'll just have to guess what you want to say: 1. You don't need to go to the bank. Yo can do it all at home on the Internet. 2. Do you want me stay here with you? (There is no need to mention "going out somewhere" as that would be redundant.)

Do you want me to not to go to university and stay with you? you could say it more simple... don't you want me to go to university and stay with you...(your original phrase sounds 'brazilian' - it is the way i would formulate the question in my native language

"You can don't" doesn't work in English. It sounds nonsensical. Just use "you can't".