@Uly
I think, there is a small difference between "has yet to " and "is yet to"
If so, "ещё не упал" looses this difference.

You're right - "has yet to" means the same as "still hasn't," and "is yet to" means something is still in the future.

Does ещё не упал mean "still hasn't fallen?"

@ "has yet to" means the same as "still hasn't," and "is yet to" means something is still in the future.
I don't feel the exact difference here.
What is still in the future, still hasn't happened.
Чему предстоит случиться в будущем, еще не случилось.

@Does ещё не упал mean "still hasn't fallen?" Да.
Это дерево (точно скоро упадет, но) еще не упало.
Метеорит (может упасть где-угодно и когда-угодно, но здесь) еще не упал (и, возможно никогда не упадет).

Я бы использовал "has yet to" в первом случае и "is yet to" во втором.
Е.g.
My son is yet to fall in a really deep hole (hopefully, never will).

There is no difference in meaning between: It's already December and the leaves HAVE YET TO FALL -or- STILL HAVEN'T FALLEN." However, ARE YET TO FALL in this context would sound archaic, if not incorrect. In your example with your son, "HAS YET to fall into a really deep hole" makes perfect sense. "IS YET to fall" is harder to imagine anyone saying or writing.

However, if you're talking about a specific eventuality COMING, APPEARING, ARRIVING (not the hypothetical possibility of your son falling in a hole) in the future, then you can use IS YET TO: The best is yet to come. -or- Keep watching - the best scene is yet to come. My favorite actor is yet to appear. The sequel to this movie is yet to follow. In all these examples, something appears. We usually use this when we ask people to be patient for what is coming.

https://books.google.com/ngrams/graph?content=has+yet+to+*%2Cis+yet+to+*&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t2%3B%2Chas%20yet%20to%20%2A%3B%2Cc0%3B%2Cs0%3B%3Bhas%20yet%20to%20be%3B%2Cc0%3B%3Bhas%20yet%20to%20learn%3B%2Cc0%3B%3Bhas%20yet%20to%20come%3B%2Cc0%3B%3Bhas%20yet%20to%20find%3B%2Cc0%3B%3Bhas%20yet%20to%20make%3B%2Cc0%3B%3Bhas%20yet%20to%20see%3B%2Cc0%3B%3Bhas%20yet%20to%20prove%3B%2Cc0%3B%3Bhas%20yet%20to%20receive%3B%2Cc0%3B%3Bhas%20yet%20to%20take%3B%2Cc0%3B%3Bhas%20yet%20to%20show%3B%2Cc0%3B.t2%3B%2Cis%20yet%20to%20%2A%3B%2Cc0%3B%2Cs0%3B%3Bis%20yet%20to%20be%3B%2Cc0%3B%3Bis%20yet%20to%20come%3B%2Cc0%3B%3Bis%20yet%20to%20do%3B%2Cc0%3B%3Bis%20yet%20to%20learn%3B%2Cc0%3B%3Bis%20yet%20to%20take%3B%2Cc0%3B%3Bis%20yet%20to%20appear%3B%2Cc0%3B%3Bis%20yet%20to%20begin%3B%2Cc0%3B%3Bis%20yet%20to%20follow%3B%2Cc0%3B%3Bis%20yet%20to%20seek%3B%2Cc0%3B%3Bis%20yet%20to%20become%3B%2Cc0

my head hurts...
I understand the leaves: they have to fall and have yet to fall.
However, my son has yet to fall, although he doesn't have to.
And, the leaves have yet to fall, they will sooner or later - this is still in the future (you used this explanation for 'is yet to').

The difference is still far too evasive for me to catch it...

ETA: I replied to your -2 comment. I'll deal with the last two tomorrow. It's too late here...

Now I understand your confusion. The verb HAVE in this construction is not the same as in the expression HAVE TO (должен). There is no sense of obligation, just to the absence of an expected action. So, for example, "he has yet to write me" doesn't mean Он ещё должен писать мне письмо. It means (Как ни странно) он ни раз не писал мне. "My son has been in England for two months and has yet to write me." This is the same as saying "my son has been in England for two months and funny enough he hasn't written me once."

OK, thanks. I think I grasped it now

Great