You said earlier your mom lets her cat out all the time. Now she doesn't?
Anyway, please do not let your kitten(s) outside unless they are on harnesses and with you all
the time. The outdoors, unless in an area that is completely closed in, is not a safe place for cats. Ever. They are escape artists that can and will find a way out. I was hoping by answering my questions you would see it is not safe to let them out.
Knowing you live in an apartment where you are not allowed cats - I am not sure it is a good idea to bring in another one. What happens if the landlord finds out you have cats? Do you just get rid of the cat(s) or do you move to an apartment that allows them?
I gave you a website to read in an earlier post about introducing cats.
Please avoid feeding tuna to your cat except for treats. It is too salty for kittens/cats and is not a good diet. As an occasional treat it is ok if it is packed in water and not heavily salted. Your kitty needs a good canned food to be at his healthiest. Not dry food or human foods.