We have no way of knowing if her J1 is subject to a two year home country residency requirement. She would have to check her visa or, if she can't figure it out from that, check with her sponsoring organization.
She can't seek a K1 visa while she's inside the U.S.
To marry you, she and you would follow the laws of the state in which you reside for obtaining a marriage license and marrying. If she's subject to the two year foreign residency requirement she must serve that out or get it waived before she can adjust her status; so it's important to find out.

