When Brian tells Wendy she'll be even more pleased to see how he's solved his problem, he says

Brian - A fyddi di'n falchach byth o weld beth wnaf i hefyd.
You'll have come across byth with the meaning - 'ever or never'. But byth can also be used to intensify the meaning of a comparative adjective. So, balchach byth means 'even more pleased' or 'ever so much more pleased'. Here are some other examples:
gwell byth which means 'even better or 'better than ever'
gwaeth byth which means 'even worse ' or 'worse than ever'.

When Jenny realises that Brian hadn't heard the news of Arwyn's mother's death she says: 'Dwyt ti ddim wedi clywed chwaith...'
'Chwaith' is used instead of 'hefyd' for negative statements.
So you'd say 'Rwyt ti wedi wedi clywed hefyd' for 'You've heard too' but 'Dwyt t i ddim wedi clywed chwaith' for 'You haven't heard either'.
Listen to some other examples here:
Mae hi'n dod hefyd - She's coming too
but
Dydy hi ddim yn dod chwaith - she's not coming either
Dw i'n mynd hefyd - I'm going too
but
Dydw i ddim yn mynd chwaith - I'm not going either.

Jenny tells Brian that Arwyn's an only child.
In Welsh you'd say he's an unig blentyn.
Unig is one of the few adjectives in Welsh which comes before the noun.
Other examples are hen lyfr - an old book, prif ddinas - the chief city or the capital, hoff le - favourite place. If unigfollows the noun, it means 'lonely'.
Remember this Welsh phrase: 'Mae unig blentyn yn blentyn unig' - An only child is a lonely child.