How a cat reacts to being left alone really depends on the cat's personality. Unfortunately, there's no a good way to tell how a cat will react until you know its personality and/or it is in a particular situation. Some cats may be fine on their own for a couple of days, but others will become very destructive and can be a danger to themselves and to your apt. It would be a shame for you and a possible new cat if you had to give the cat back because the cat couldn't work with your schedule
If you really want a kitty, is it possible to have someone stop in to check on the cat? If you get a cat and he/she is the type that can be left alone for 2 days (with plenty of food, water and litter sources), then he/she could be ok for a couple of days alone. I wouldn't want to routinely leave a cat (or cats) alone for a couple of days each week though (without at least a visit or two from someone).
I have tested my cat and he paces himself with his food, is ok with two days worth of 'stuff' in his litter box, and when he is left alone during the day, he isn't destructive to my apt. I think he'd be fine if I went away for two days and couldn't get a friend to stop in. But, I've had my kitty for a while so I know his personality.
On the other hand, a friend's cat could never be left alone for a couple of days. If the litter box is not clean, he will do his business outside of it. And, he is forever climbing on things and trying to pull things down to play with. He'd tear her place apart and maybe even hurt himself.
As for the space a cat needs, there should be no problem in having a cat in an apt. You'd just want be sure to give the cat some good playtime.