Aye, feminine of the 2nd declension add -e (and slenderize if it isn't slender), but you don't slenderize without adding -e.
If Cairméal were feminine, in the genitive it could (in theory) become Chairméile or Chairméala or Chairméal but not Chairméil because only a masculine noun would change this way.

Bríd is in the 2nd declension here, that's why it becomes B(h)ríde in certain phrases.
I'm not sure you'd use that genitive everytime though, for instance if you say "Brid's house" or "Brid's dog", I'm not sure you'd say "teach Bhríde" nor "madadh Bhríde". It might be used only when talking about Naomh Bríd things (Lá Fhéile Bríde etc).

Our Bríd will tell us

_________________
Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Thanks yeah that makes sense.

Ok one eile, how would I say 'The Proud' as in a hint of arrogance pride. The word I have is Uabhar. It would be a nickname for a man, I am thinking An tUabhach? Ceard a cheapadh?