'I went' and 'I have gone' are two different tenses in both Welsh and English:
- es i - I went (simple past tense, covered later in this course)
- dw i wedi mynd - I have gone (present perfect tense)
This is explained in the notes for the section 'Wedi' - https://www.duolingo.com/skill/cy/PastTens1/tips-and-notes
A: "Has anyone gone to that new restaurant yet?"
B: "I've gone"
"Been" might sound better in English here but "gone" works.
One of the weaknesses of Duolingo is that you're learning sentences or partial sentences outside of context, a bit like grammar books from last century. In those books, sometimes a sentence wasn't even one you'd ever hear ("The pen of my aunt is on the bureau of my uncle" kind of thing), but more just to practise a particular grammar point. This is why Duolingo have introduced stories on some of the bigger courses, I guess. Until they arrive for Welsh, I wouldn't try and find an ideal context for everything - that's more the kind of thing you'd get in a class, book or conversation group - more like real life!
I agree with you Dw i wedi mynd "I've gone" on it's own usually sounds weird, but it's probably here mainly to make sure you remember to distinguish it from Dw i'n mynd "I go / am going", Ro'n i'n mynd "I was going / used to go" and especially Es i "I went".
Maybe as in "are you going? No I have already gone" Going is when you are about to leave have gone is you already left. (I'm thinking about people talking about a breakup)
I guess basicly you can compare it with I have left.
It is hard to explain, in my language it makes sense, so then to explain in English why it is different in english is not so easy. (Just as the different tenses in English aren't easy to understand/ learn for speakers of other languages. I remember the different use of tenses was what my classmates used to struggle most with.)