A fairly basic question about cael and gallu. ‘Can I help you’ seems to be ‘Ga i’ch helpu chi’. You just wouldn’t say ‘Alla’ i’ch helpu chi’, am I right? But I’m thinking ‘I’m sorry but I can’t help you’ would be ‘Mae’n ddrwg gyda fi, ond alla’ i ddim eich helpu chi’ and you wouldn’t use cael here, right? Perhaps it is like the little-observed distinction between ‘may’ and ‘can’ in English, which I remember my primary school teacher trying so hard to preserve. ‘Please, Miss, can I go to the toilet’. ‘Well, Johnny, I certainly hope so, otherwise you’ve got serious problems, but I think you mean ‘May I go to the toilet?’’ She would then proceed to lecture us the niceties of the modal auxiliary, by which time the poor kid had probably wet himself anyway. Now that was proper teaching…
yes, it’s this 
As an aside, ‘may’ comes from the Old English word for ‘to be able to’ (‘can’ was ‘to know how to’, d’ya ken?): your teacher was perfectly happy for mediaeval children to ask if they were able to go to the toilet, just unwilling to extend the same pragmatic courtesy to modern ones.
She sounds like a bully. 
Hang on, am I right in thinking that the following is correct?
Cael is to have or get: Cael frecwast (have/get breakfast)
Gallu/galla is to be permitted to (may); also to be able (can) in S Wales, with the “G” omitted in a question.
Medru/medra is can (able to) in N Wales; fedrai in a question.
Edited: Phew, I think that’s it.
Yes, but can also imply permission in a slightly colloquial sense - I get to eat a special breakfast at weekends.
And I think e.g. “Ga i baned of goffi plis?” maps quite well on to the (relatively) modern usage that has come into British English among (relatively) young people of “Can I get a cup of coffee please?”.
(Which doesn’t sound quite “correct” English to my old-fashioned ears, but it’s heard a lot nowadays).
I suppose you could also say “Allai i gael paned o goffi plis?”, but I don’t know if anybody does.