I'm not always sure when a pronoun (such as הם here) is needed and when it can be omitted. I can see that it occurs when the noun is the subject of the sentence, but it seems to me that sometimes it's used and sometimes it's not. Is there a rule, or is it just a matter of context/usage? So, in this case, would בקבוקי היין האלה יקרים be acceptable?
Yes, that would be acceptable. You usually omit the copulative pronouns, if the predicate is an adjective (הַגֶּ֫בֶר עָיֵב "the man is tired") or an adverbial (הַגֶּ֫בֶר בְּתֵל־אָבִיב "the man is in Tel Aviv"), but you can place it, if the subject is very long (כׇּל הַפַלַפֶלִים הָאֵלֶּה הֵם קָרִים "all these falafels are cold"). You have to put it in sentences, where the predicate is a noun (הַגֶּ֫בֶר הוּא רַב "the man is a rabbi"), but not, if the subject is a pronoun (הוּא רַב "he is a rabbi")
Pay attention, please. In this part there are a problem. I was pushed out many times and can not move forward. In the next part is the same problem.