For young kids, "love" can mean so many things and in this case probably means "I like you". I wouldn't be concerned about it personally and would be happy that she likes you...it could be a lot worse..she could be saying "I hate you" I have had daycare kids say they love me before and I don't correct it...who am I to tell them who they love or don't love...plus I know kids don't attach so many connotations and baggage to the word.
As for the playing, she will get it with time once she finds her place in the group and gets used to playing independently. It takes time if they haven't been in daycare before.