I would accept an invitation but insist that I help or bring something. Then make myself useful by coming early to help and then help to serve and clean up. I would also say that I am no longer a “guest” but a good friend or extended family so I feel quite at home here, and must show my hakaros hatov by doing my share. Of course that is in lieu of the hostess having prepared extra help herself.
As far as taking someone’s phone number, be gracious and take the number. Then say, that is very generous of you. I will do my best to keep in touch, I have a very full schedule and am not very good at adding new friends at this time.