litter box then the number of cats you have. Now if someone has a lot of cats that is impractical so I would say have a few scattered around the house (utility room, bathroom, whatever). What is important is to clean out the litter box frequently and not let the pee and poop pile up. Letting the litter box go to long without being scooped out might cause problems (and I wouldn't blame the cat).
With just one cat all you should really need is one litter box. If she is wanting to be a solo cat that should be fine. I agree with your friend, that problem #2 should go away. Now if the problem should continue, she might be really picky about her litter box I would recommend scooping it out at least once a day. I had a friend who did not do that and every time I would cat sit for her the first thing I always did was to scoop out the litter box which always nasty when I got to my friend's house.
We have a lot of cats in my neighborhood and one of them decided to move in last year (yup he became my freeloading roommate 
) and he is an indoor/outdoor cat (only because he used to be an outdoor cat) and I keep his litter box in my utility room. With winter coming on he is indoors far more than outdoor and I think that he will go outside to do his "chores" and them come back in so I don't have to clean out his litter box that often. Although if we get enough really cold days his outdoor time will dwindle now that he has discovered the good life.
Regarding food, I have had to put the food dish on a table to keep the dogs from eating it. I have two water dishes out that both the dog and cat use (one in the kitchen and one by the dog's bed in the living room 
. What can I say, the dog is bossy and spoiled.
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