Answers

You can, but you should prime first. I recommend a good bonding primer like Stix or XIM

Please do yourself a favor and don't beleive "paint and primer in one". All that refers to is painted surfaces that have minor stains or a large color change. There is a reason that every paint store carries numerous primers. That being said, I echo the thoughts of the previous participants and say to use an oil primer that is specifically a stain blocker. These smell very bad but the smell will dissipate quickly and can usually be recoated in an hour.

I would echo what Steven says. Generally, flat paint is not washable. If you look at the cleaning instrctions, it will talk about being "scrubbable". This means you have to scrub a layer of paint off to get the dirt out. That is why the Magic Eraser works for a while. Ultimately, if you can simply use a degreaser and a rag, do it. If not get ready to paint with a "washable" flat or matte finish. Benjamin Moore also makes a very washable matte finish called Scuff-X.