Yes you can paint over Oil Based Paints. I suggest using primer or Kilz over top of the old paint first. Put a coat or two of that on and then paint with your new latex paint. There should be no problem and your paint should stick nicely to your walls.
Not directly. First scrap any loose or peeling paint then cover the oil based paint with a primer suitable for use over oil paint (check the label). Then paint over the primer coat with your latex paint.