I think I’ve worked out there are three ways of saying something is happening in the future. For example, if I am going somewhere tomorrow, I can say:
Dw i mind i fynd
Bytha i mynd
(I may not have got these exactly right, but hopefully you get the general idea.)
What I’m wondering is, does one of these sound more ‘natural’ to a native speaker? And would you use different ones in different occasions? For example, I notice you taught us “awn ni” for “let’s go” or “shall we go?”, so is it natural to use that form that way, but maybe not where you’d say in English, " we’ll go" or “we’re going”??
Not really, they’re all used pretty much equally. The differences are so subtle they don’t make that much difference (and it’s the same in English):
Dwi’n mynd i fynd = I am going to go
Bydda i’n mynd = I will be going
Af i = I’ll go
The short form “awn ni” for “let’s go” is because in English ‘let’s go’ is a kind of idiomatic phrase, and for “shall we go”( = are we going?) because this is the question in the short verb form (in long verb form, it would be “ydan ni’n mynd?” (are we going?), or “fyddan ni’n mynd?” (will we be going?)
I’m not a native or habitual (or even particularly competent!) speaker but I’ve read that the short-form future tends to be used for the more immediate future, while the long form (using bydda + yn + verbnoun) is for the more distant future. Christine Jones’ Welsh Grammar You Really Need to Know gives the following examples (Ch. 20, p. 174, 2015 edition):
Gofynna i iddo fe nawr = I’ll ask him now
Bydda i’n gofyn iddo fe eto cyn y penwythnos = I’ll ask him again before the weekend
But, as @siaronjames says, the difference is quite subtle and probably not worth getting hung up on.
There is another version of the short-form/immediate future, which uses the future tense of gwneud (to do/make) + verbnoun (which will be soft-mutated):
(Gw)na i ofyn = I’ll ask
Na i dalu = I’ll pay
The construction with ‘mynd i wneud rhywbeth’ seems to directly correlate with the English ‘going to do something’.