Which article is more appropriate here if we speak about one certain person? As I understand it, if we speak about an indefinite thing - invisible barrier - we need to use a/an. Right?
There is an invisible barrier for him to make small talk.
Use "a/an" when referring to an unspecified thing. Use "the" when referring to one specific thing.
Use "the" if there is only one of something in existence, like "the universe". Also use "the" when there is only one of something that makes sense in this particular context. Like if I was talking about United States politics and then referred to "the president", presumably I mean the president of the US and not the president of France. I would say "the president" and not "a president" because the US has only one president. At least, only one at any given time. If in context I could be talking about any one of many past presidents, I would say "a president". Like, "Abe Lincoln was a president of the United States." But if the sentence adds additional details that narrows it down to only one possibility, it becomes "the". Like, "Abe Lincoln was the president of the United States in 1862."
Use "the" if which one has been specified in context, like, "Bob sat in a chair. The chair was orange."
That last example is a common pattern: At first mention something is "a". But now we've identified it, so all future references are "the".
Tangent: The wording of your sample sentence is awkward. In "... for him to have small talk", "for" means "to enable" or "to accomplish", like, "This tool is for removing screws." So the sentence, taken literally, means that he uses the invisible barrier to enable him to have small talk. Which I think is the opposite of the intended meaning. I think the intent is something more like, "There is an invisible barrier which prevents him from having small talk." But anyway ...
In this case, at the time you begin the sentence the invisible barrier has not been identified or introduce. It is this sentence that introduces it. So you say "an invisible barrier". In following sentences, now that you have identified the barrier, it would be "the". Like, "There is AN invisible barrier that prevents him from having small talk. THE barrier has surrounded him since he was in high school."
Yes this is the correct article. However your sentence does not sound idiomatic. for him is a confusing verb choice in this context. A more natural way to phrase this idea could be something like
There is an invisible barrier preventing him from making small talk.