If he wants to cheat on his girl this should send you a big red flag to start. If he had genuine feeling that could actually go somewhere, he would end it with the girl first and take you on a date, not just a hotel room. As for the dreams... You need some closure.
It is a cross between a silky (looks like a large yorkie) and a poodle.
Start by using a setting lotion or styling aid with some stick. Roll the hair and let it air dry thoroughly or put her under a hood dryer if possible.