he wants to be married to her and that he loves her
Because Juliet wants to know his name and so asks the Nurse, her family servant and mother figure, to find out for her.
She tells him not to mess with Juliet, that he had better be sincere in his wooing.
To meet with him and for them to get married
Once Romeo is exiled, Nurse tells Juliet to forget about Romeo and marry Paris.
because she new she was in love with him and didn't want to split them up.