As far as point 2 goes, in Victorian England members of the nobility would often be granted the title of Lord or Lady (Ladyship was usually bequeathed automatically to the Lord's wife). The name that followed his title would be that of a place in England, hence the monikers Lord and Lady Bracknell. In this play Lord and Lady Bracknell would still possess a surname, but have become known by their titles. Gwendolen, as their daughter, is inelegible for an automatic title, thus retaining 'Fairfax' as a surname.
And yes marrying your first cousin was actually a good thing back then... kept the wealth within the family concerning dowries and suchlike.
I think Wilde was being ironic when Cecily seemingly forgets her earlier obsessions with the name Ernest... just wanted to show how fickle people can be!