"loud, and long, and clear!"
So everybody can hear!
Is the r prounced like an f in chwerthin?
No. In Welsh the letters are pronounced as they are written, with very few exceptions.
(A common exception is the noun eisiau (need, want), which is almost almost pronounced isha, isho, eisha, etc, according to where you are in Wales.)
I'm glad somebody does. </eeyore>
Is Irish "gáire" buried within this word?
Maybe. A lot of 'laughing' words are similar or related in the world