The up to date version of this course gives 'dyn ni'n' as the best translation, since it is a bit more standard than 'dan ni'n'.

If you're only seeing 'dan ni'n, then if you delete your browsing history (or install a new browser just for Duolingo) or update your app you should see the latest version of the course.

However 'dan ni'n' is the standard spoken form in North Wales and is accepted on the course for all sentences using 'we are' or 'we do'.

No, that is slightly incorrect and has a different meaning.

'Dyn ni'n mynd i gerdded' = We are going walking/We are going to walk.

Thus we are going to carry out the action of walking.

'Dyn ni'n mynd am dro' is an idiom which means literally 'We are going for a turn' so this is a description of a social activity.