My mother says that she has an allergy to cats. After being over to friends that have cats houses, I questioned her and she said the allergies only start after being exposed to the cats for a long time. Is this a real allergy or does she just not want to get a cat?
In my experience, it's possible to have a mild allergy that doesn't manifest until after a period of time.
Typically, "allergy to cats" is actually an allergy to cat dander, saliva, etc. (http://www.webmd.com/allergies/guide/cat-allergies). Allergies can have a large range of severity to the very mild through to severe enough that being in the same house as a cat compromises someone's breathing (I've known people like that).
Personally, I'm mildly allergic - I have three cats, and I have to remember to wash my hands after petting them or if I rub my eyes afterwards I'll have sore, itchy eyes for quite a long time. I'll also wind up sneezing a lot more if a cat gets in my face too much.
It sounds from your description like your mother is mildly allergic, and the allergy symptoms don't manifest until there's a high enough concentration of the allergens in her system. If she doesn't want to deal with allergy symptoms caused by having a cat in the house, that's her decision.
This really depends. Person who suffer from allergies by specific breed may not be allergic to some other breed and vice versa. Allergy to cat is very specific and influence different people variously. Interestingly long-term exposure to cats may cause both increasing or decreasing allergic symptoms. Exposure to cats impacts people differently. You may find more about this on the following link: Hypoallergenic Cats ... see hypoallergenic cats basics and interesting facts about them.