Michelle asks Brian 'Beth wyt ti'n feddwl oedd e'n feddwl?'
Normally the verb doesn't mutate after 'Wyt ti'n?'. You'd say 'Wyt ti'n mynd?' not 'Wyt ti'n fynd? But in a question beginning with 'Beth', or its abbreviated form 'Be', the verb must have a soft mutation. So Michelle asks quite correctly, 'Beth wyt ti'n feddwl?'

This rule applies to other persons as well. So you'd say:
Beth ydych chi'n ddeud? What are you saying?
Beth mae Brian yn weld? What does Brian see?

When Chris asks Brian why he'd taken so long to come, he replies:
Brian - Mi ddoish i gynta' ag ô'n i'n gallu . . . (Mi ddois i gyntaf ag oeddwn i'n gallu...)

You've already learnt 'cyntaf' meaning' first', but cyntaf can also be used with the meaning 'as soon as'. So when Brian says, 'Mi ddoish i gynta' ag o'n i'n gallu', he means he came as soon as possible, not he was the first to come. Another idiom with cyntaf is 'gorau po gyntaf', which means 'the sooner the better'.

Brian tells Arwyn how much Jenny had enjoyed her recent trip to Africa.

Brian - Dywedodd Jenny ei bod hi wedi cael amser wrth ei bodd draw yn Affrica efo chdi...
Arwyn - Dw i'n cael amser wrth fy modd yn Affrica hefyd...

In that conversation, you heard 'wrth ei bodd' and 'wrth fy modd'. This is a very common idiom meaning 'delighted', or literally 'at one's pleasure'. It has the normal mutations you'd use after fy, dy and ei meaning 'my', 'your' 'his' and 'her'.

So, if referring to youself, you'd have to say 'wrth fy modd', meaning 'I'm delighted'. But if you were reporting that Arwyn, or any other man, was delighted, you'd have to say 'wrth ei fodd'. When referring to women or the plural in general there's no need to mutate. So you'd say, 'Mae Jenny wrth ei bodd', 'Maen nhw wrth eu bodd'. Stick to 'bodd'. I'm sure you'll be 'wrth eich bodd' to hear that!