No, the milk is not universal.Breasts produce milk designed to meet the needs of THAT infant whose conception and birth triggered it's production. So, there will be some slight differences in the levels of antibodies, fat content, etc.
Milk produced right after birth, colostrum, is much different than the milk produced at a week old, month old, six months, etc. I'm not sure they would be able to have colostrom on hand at milk banks, however, because it's only expressed for the first few days of babies' lives. I would imagine they would have milk from lots of other stages though. Some women produce a lot of milk, enough for three infants, some produce only enough for their own.
Healthy human breast milk is always superior to artificial formulas though, despite the varied levels of antibodies and such.
It's too bad they have to pasturize the milk, it kills off all of the live enzymes. I guess it's best to be as safe as possible though.
If a child keeps nursing, or as long as the glands are stimulated, the milk keeps coming. So, a woman who had given birth and weaned her own children could still pump her breasts if she wished to.
Some women can get hormonal injections to trigger lactation, even if they haven't been pregnant. When an infant starts suckling, the milk comes in naturally without the continuation of hormones.... though I imagine there are some cases where hormonal stimulation is continued. This is especially nice for mothers who have adopted infants and want to breast feed.
Often, donated milk is supplemented through a tiny tube attached to the nursing mother's nipple and while her glands are being stimulated and while she is producing some milk, the infant gets an extra shot of the donor milk.
There have even been cases where men have lactated, either spontantiously or through suckling... though this is very rare.