Yes! you can have sex during period. I would be more caution as to if she has particular pains during that time, to be more concerned about her pain. Now, most men just think the bleeding is gross and don't want to do it during that time. I would definitely be cleaning well afterwards, just because dried blood is not really good.
Otherwise, the blood mostly provides extra lubrication (at least how i see it), so enjoyment is really all up to you. She may not feel it as well or as much as she would when she is not having a period.
As for getting pregnant, well it could still happen. You should be practicing safe sex at any rate, regardless of the time of the month.