I have a questiom regarding the trilled R. It seems to me that the R is not trilled when it is not the starting consonant of the word, but rather it is partially assimilated. I wonder if that is correct. Diolch.
r is trilled (if you can trill), no matter where it is in a word.
I always thought Carmarthen was translated with Caernarfon. Am I confusing something here?
Yes. Caernarfon is Caernarfon in English as well nowadays (it used to be spelled Caernarvon in English in the past).
Both Caernarfon and Caerfyrddin/Carmarthen have some interesting history - have a look on the web for information about them both.