Learn English – Present perfect or simple past with “for the last twenty minutes”

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.

As an American English speaker, all four examples seem correct.

The past perfect often seems to be used in American English to avoid confusion about the relationship between two past events. Where such confusion is impossible, the simple past is often used.

"I had typed ten pages when he returned." indicates typing before returning. "I typed ten pages when he returned." implies that returning is simultaneous or even before the typing.

In your examples, "by the time" serves this temporal ordering purpose, so the choice of verb tense is unnecessary.