You can translate it as ever if it's in a question or if there is some other negative word (as in "Nobody has ever climbed that mountain"), and as never otherwise.
It's not a question here and there's no other negative word such as "nobody", so "never" is appropriate here.
Both can mean "never" and both take the place of ddim in a negative sentence.
You use erioed with:
present perfect: Dw i erioed wedi mynd i sgio "I've never gone skiing"
simple past: Es i erioed i sgio "I never went skiing"
pluperfect: Do'n i erioed wedi mynd i sgio "I'd never gone skiing"
And byth is used with:
present: Dw i byth yn mynd i sgio "I never go skiing"
imperfect: Do'n i byth yn mynd i sgio "I was never going skiing / I never used to go skiing"
future: Fydda i byth yn mynd i sgio / A' i byth i sgio "I'll never go skiing"
conditional: Faswn/Fyddwn i byth yn mynd i sgio "I'd never go skiing"
You can also leave the ddim in and put the erioed/byth at the end:
Do'n i ddim wedi mynd i sgio erioed "I'd never gone skiing"
Do'n i ddim yn mynd i sgio byth "I never used to go skiing"
...and so on.
Yes, for the most part, tenses using yn have byth and the others have erioed. So I guess it's a good rule of thumb.
That said, there is one yn tense that takes erioed:
simple past with bod: Fues i erioed yn dringo "I('ve) never climbed" - not a common tense and not one taught on Duolingo, as far as I'm aware
And there's a non-yn tense that take byth:
short-form future: Ddringa i byth / Wna i byth dringo "I'll never climb"
Also, when it comes to a couple of perfectives, as a southerner I'd have no qualms using byth:
future perfect: Fydda i byth wedi dringo "I'll never have climbed"
conditional perfect: Faswn/Fyddwn i byth wedi dringo "I'd never have climbed"
I believe northerners would be more inclined to use erioed with these, at least with the conditional. (byth is more common in the south, especially colloquially.)
So in short, your rule usually works, and the tenses it doesn't work for are quite rare ones you won't use often apart from the short-form future, which is a pretty common tense.
Double negatives don't make a positive in Welsh, they just usually make it more negative. In the case of erioed it usually takes the place of ddim rather than being added after it:
Dw i erioed wedi bod yno "I've never been there"
Alternatively you can keep the ddim in if you put the erioed at the end:
Dw i ddim wedi bod yno erioed "I've never been there"
“Yno" seems to be used for “there, out of sight”, whereas “yna” seems to be used for “there, within sight”. You can point to yna, but you can't point to yno.
This only half answers your question — I don't know what you'd say if you were pointing at somewhere visible in the distance and explaining that you've never been there!