I am only correcting the points that caused questions.

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3.A.A – Пребывание в месте в прошедшем времени (= был / была / были там)
I wouldn't call it "пребывание", because "пребывание" actually means the time that you spend there (il soggiorno). I would call it "посещение" (visiting some place and leaving it).

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3.A.A.2) Мы ездили на Кавказ (the same like на Урал, на Алтай, prepositions with mountain chains and country regions should be remembered case to case, "в" or "на") (intended meaning: Мы уже бывали на Кавказе, ie been there, done that). This sentence does not show whether this is the first or not the first time they visit the place, so "уже бывали" is not relevant here. I would explain it simply as "побывали", "съездили" (visited it on this occasion).

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Examples
3.A.B.1) Игорь ходил в кино.
Possible contexts for this example
– Igor watched the film. Now he's back home.
– Igor watched the film. Now he's heading somewhere else. - This sentence does not say if he is heading somewhere else now, he may already be somewhere, e.g. in a cafe. It can be explained in a particular context by a further sentence, but here it is not important.
– The cinema was closed: Igor left. Honestly, this option is a bit weird, because "ходил в кино" means that he actually saw the film. If Igor "ходил" somewhere, it means that he DID VISIT this place. But he didn't, he did not even enter the cinema, just stopped by. So here I would say "Игорь хотел пойти в кино, но кинотеатр был закрыт". Or, alternatively: "Игорь ходил к кинотеатру, но сеансов на ближайшее время не было, и он пошел гулять".

Continuation

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Examples
3.A.C.1) Игорь шёл на работу. (and he's still at his workplace)
3.A.C.2) Игорь шёл в кино.
Possible contexts for this last example.
– When he arrived, the cinema was closed; he's still there, waiting for the cinema to open.
– He left heading to the cinema, but on his way ру met a friend and together they decided to go to the park; when they will say goodbye, Igor will go to the cinema, to watch a later show. The speaking person speaks while Igor is still spending time with his friend (she knows about it), but she isn't interested in saying anything about the trip to the park.

Regarding both of the above sentences, "шел" can only mean the process of walking, being on the way to. With it you can either describe this process "Игорь шел на работу и слушал музыку", or an interrupted action "Игорь шел на работу, когда ему позвонил клиент". Another example: "Я шел в парк, но передумал и пошел в книжный". It's like Past Continuous in English. In both cases there is a need in giving more details, because as such these sentences are not complete logically.

So, in 3.A.C.1. I do not see why he should still be at his workplace, the sentence and the explanation do not fit well together here. Because if he "шел", he either has already come, or decided to go somewhere else.

3.A.C.2 - I agree. But I see both contexts that you give as a single one, an interrupted action (in the first case by the closed cinema, in the second case by meeting a friend). In Russian, I would imagine the following full sentences:

a) Igor: (standing by the cinema to a friend he just met) Я шел в кино, но просчитался со временем, кинотеатр пока закрыт.

b) Igor: (calling his Mum) Я шел в кино, но встретил друга, и мы вместо этого идем в парк. (And I do not see the information on whether he will return to the park later or not really important).

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3.A.C.3) Вчера в 5 часов она ехала в аэропорт. (цель несущественная) Yes, I agree. Here the accent on the motion that was happening at a certain moment in the past is more important than the destination.

LEVEL 3.A – Конкретное однонаправленное однократное движение

3.A.A – Пребывание в месте в прошедшем времени (= был / была / были там)
Usage: Глаголы неоднонаправленного движения

Examples
3.A.A.1) Я вчера ходила в кино. (intended meaning: Я вчера была в кино -- correct)
3.A.A.2) Мы ездили на Кавказ! (intended meaning: Мы уже бывали на Кавказе, ie been there, done that)

Мы ездили на Кавказ -- We have been to Caucasus. It has an abstract experiential meaning similar to perfect tenses. It is not a concrete motion at all.

3.A.B – Цель движения уже неактуальна
Usage: Глаголы неоднонаправленного движения

Examples
3.A.B.1) Игорь ходил в кино.
Possible contexts for this example
– Igor watched the film. Now he's back home.
– Igor watched the film. Now he's heading somewhere else.
– The cinema was closed: Igor left.

Игорь ходил в кино. If it's not the same as 3.A.A.1, than it simply means "Igor went to the movies". Simple statement of the fact that took place in the past. Doesn't imply anything else.

3.A.C – Все остальные случаи (включая случаи, когда цель несущественна)
Usage: Глаголы однонаправленного движения

Examples
3.A.C.1) Игорь шёл на работу. (and he's still at his workplace -- wrong)
3.A.C.2) Игорь шёл в кино.
Possible contexts for this last example.
– When he arrived, the cinema was closed; he's still there, waiting for the cinema to open. -- wrong
– He left heading to the cinema, but on his way ру met a friend and together they decided to go to the park; when they will say goodbye, Igor will go to the cinema, to watch a later show. The speaking person speaks while Igor is still spending time with his friend (she knows about it), but she isn't interested in saying anything about the trip to the park. -- wrong

Игорь шёл на работу/в кино -- Igor was going to work/to the movies (when something else happened); progressive/simultaneus meaning. Eg. Игорь шёл на работу, когда на него упал метеорит.

You can say "Игорь ушёл на работу" -- Igor left for work (now he may be there or not)

3.A.C.3) Вчера в 5 часов она ехала в аэропорт. (цель несущественная) correct
3.A.C.4) Они медленно шли. (цель несущественная) correct. You can also say Они медленно ходили with the same meaning. Eg. Они медленно ходили по парку.