"Regrets" rather than RSVP - ie if I don't hear from you I'll assume that you're coming - only reply if you can't attend (and then it is due to a previous engagement).
'At home' is short for drinks and nibbles (finger food). It would be appropriate to take a small gift (flowers and/or decent chocolates). As to dress - probably smart casual - chinos and a shirt for you and a dress for Mrs MM - if you're not sure then ask before hand; no shame in that.
Do write a short thank you note; this should be from Mrs MM to Mrs Bloggs; just say thank you for her hospitality and company and how nice it was to meet everyone (written in the first person).
Arrive about 15 minutes late and don't be the last to leave.