Hi, a Chihuahua would be just fine in a apartment. You can pad train it and you wouldn't have to worry about taking it outside to go. But if your GF wants a cat maybe you should agree one one or the other 1st. Plus Chi's tend to live a long time (compared to most other breeds I'd say)
Hi, Welcome to the forum. First of all, I have both a cat and 2 dogs. If you get both at or near the same time, they will 'grow up' together and be fast friends. Kittens should have their nails cut back slightly, so that they won't get the puppy's eye by accident. Other than that go for it!
I agree with Susan and Ari. Chis don’t have to go out as they can be trained to go inside. Bringing them outside is an option. In addition, as was already noted, you can have both cat and dog if you raise them together. Chis can live as long as 20 years. Taking on any animal is a commitment.