All landlords want to know if you have the where with all to pay your rent. Many people want what they want and dont have any money sense so that if they moved in, it would be a disaster for all concerned or that they have some way of making money they don't want to talk about.
A building (apartment) doesn't but landlords do.
Not all. Some won't care about income if you have good credit historyand can prove net worth. Others don't check anything at all if you prepay a year's worth of rent.
Apartment owners/managers like to know you have some way to pay for your apartment. Makes sense, right?
Complexes, usually yes. Private LL's, sometimes not.
No many apartment are rented by owners or even companies that will only care if you have money.
However they also may not be the best choice for a quality place to live.