1, 3, and 4 are correct!
I will get you something is very common. I will bring you something has to do with the direction.... I will go to the kitchen and get it, but the I will bring it to you. If I take it, I am taking it from you. So after you drink, I might take your glass back to the kitchen for you.
4. Fetch means to go and get something. Sometimes it is a condescending word (because we use it as a command for a dog to fetch a stick) but not always. I might say "let me fetch that for you." It is less common in this situation, but it is still correct. Technically it means to go get something and bring it back.
Good questions!