when you say “I wrote my article yesterday,” does this imply that at this moment you have a finished article or not?
Yes, you finished it. Otherwise, as you say, you would say something like "I started to write my article yesterday". In that case, 'started to write' has finished even if the article hasn't.
What about present perfect? Does it imply completeness?
No, it doesn't. Present Perfect is 'until now' or 'relevant now'. It says nothing about what happens after now, though context might. For example:
"I have worked in that factory" implies (by using 'that') that you no longer work there. Maybe somebody is asking you what is inside, and you have relevant knowledge because you have worked inside the building.
"I have worked in this factory for ten years", but this is your last day. You have worked here until now.
"I have worked in this factory for ten years", so you know where the toilets are and don't need telling. Unless you get sacked you will continue to work here.
do I have to use past continuous to emphasize the incompleteness of action?
If the action is incomplete, you use present continuous. Past continuous is for a finished action.
In your example “I was watching this film”, the action - the watching - is complete. You are not watching it any more. Whether you completed the film or not doesn't really come into it, as the film is not the action.
You don't normally use Present Perfect with stative verbs (have, be, like, seem, prefer, understand, doubt, know, etc.) Here's a longer list - in general, they apply to states that last for some time.
In some contexts, such as "How long have you had/been having these symptoms?", there's no real difference. Arguably, been having calls more attention to the fact that you're still having the symptoms, but I doubt many people would consciously either make or hear that distinction.
A "rule of thumb" for to have is: when it means to experience, you might want to use Present Perfect; when it means to own, you almost certainly don't.
Here's an example for to be using the "slightly unusual" Present Perfect in a construction which is perfectly valid, and is probably the most succinct way of expressing the intended meaning...
By now the new cook will have been being introduced to her duties for several weeks.
Best Answer
Even though you would not use "They've gone" in your second sentence, note that you could say "They went" in your first sentence:
and the wording need not change if you are not sure:
("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":
but "has gone":