If I don't know an action is completed, which past tense do I use?

Even though you would not use "They've gone" in your second sentence, note that you could say "They went" in your first sentence:

They went away. They'll be back on Friday.

and the wording need not change if you are not sure:

They went away. I think they'll be back on Friday.

("went" works even though they are still gone because the action can be seen as completed in that there is only one moment that you leave).

But in your second example, "back at home" necessitates the past simple instead of present perfect because the action cannot be ongoing if they are back at home. Even if you are unsure ("I think they are back at home now"), you cannot use present perfect because of the implication that the action is not complete.

In your example dialogue, then, you could say "He went to the shop" whether you believe he is still out or not, but "has gone" only if you believe that he is still out.

eg, "went":

A Hey, where is Mark?

B He went to the shop, but I think he's back home now. / He'll be back in an hour. / I think he'll be back in an hour.

but "has gone":

A Hey, where is Mark?

B He has gone to the shop, but I think he's back home now. / He'll be back in an hour. / I think he'll be back in an hour.