Translation:In the evening
If nos = night, and noswaith = evening, then shouldn't "in the evening" be gyda'r noswaith?
You only really use noswaith when saying Noswaith dda. If you want to refer to either the evening or night otherwise, you'd use nos. If you're counting "an evening" or "a night" or describing it with an adjective, they you use noson.
No, "At night" would be "Yn y nos", as in "At night we sleep"="Yn y nos dan ni'n cysgu". Whereas "Gyda'r nos" is "in the evening" e.g "In the evening we cook dinner"="Gyda'r nos dan ni'n coginio te/cinio".
I'm not sure that's a distinction that everyone makes. Geiriadur Prifysgol Cymru has gyda'r nos as both "in the evening" and "by night".
when I hover over the 'r in the text, I hear a phrase I don't understand at all - can anyone translate it for me?
This doesn't feel right to me nor a few fluent speakers I've asked. They all told me it should be "Yn yr nos". Is this a north walian saying as from experience they do tend to have weird sayings that aren't the real translations.
As EllisV says, gyda'r nos is a widely used set phrase for both 'evening' and 'in the evening'.
You will find examples of its use if you look on the internet and if you look up 'evening' in a dictionary.
You will come across a lot of set expressions in Welsh that are not literal translations. There are also many dialect expressions from regions all over Wales, but this is not one of them.
Nor are the several Welsh dialects 'weird'!
Do northerners also use gyda here because it’s idiomatic? Or maybe efo'r nos?
Gareth King, in his Modern Welsh: A Comprehensive Grammar, says this about efo:
In the S[outh] it is always replaced by gyda, a word which, in turn, is virtually unknown in the N[orth] (except in the set phrase gyda’r nos at night).
gyda might be less used in the spoken language in some parts of Wales than in others, but it is certainly not 'virtually unknown', any more than efo is!