This is common among players here.

You guys helped me to understand the rules of priority, but there is something i would like to know.

Case A)
I am playing the Sensei Top Ability to look at the 3 cards, and in response i do it X times, so I can look deeper into the library.

I personally think that it is impossible to stack Top's ability to go deeper into the Library. No matter how many of them are stacked, they resolve each one by one allowing to look at top 3 cards for X times. However some people here think so.

Case B)
I am playing a spell when opponent say "In response i am playing spell".
This is bit more complicated.

Am I supposed to pass priority at all times? (I guess NO, it depends on me when i pass the priority?) Is there any difference if its my or opponents main phase?

The opponent has revealed card, paid mana cost before i passed the priority. However i want to continue play my spells before i pass the priority. Is the opponent allowed to untap mana and get back the card on hand?

Case C)
I am playing MOM, Then i pass the priority to opponent asking him if he wants to respond. He says no. Then i continue playing another spell, lets say something instant. Now the opponent announces "i am playing counterspell on MOM" because he realized something which was not so obvious before i played the second spell.

At moment when the opponent announced he responses the MOM was currently not on stack but on battlefield (in play). Am I right? Even in situation when I did tactically error because i wanted to play both spells at once i cannot take the situation back because MOM already resolved.

Case D)
Player puts 2 spells on stack, his opponent says that he reacts on the first announced spell, then player draw back to hand second spell. Just say that card has been revealed. Player has passed the priority to opponents request in middle of playing next spell.

Case E)
Its end of my turn. I ask the opponent if he wants to do at the end it. He says no. Do I receive the priority back or no? Is it still my turn, or i have to announce end of my turn.

Case F)
its end of my turn. I ask the opponent if he wans to do at the end of it. he says yes and he do some actions, however I want to react, however opponent has announced his next turn.

Main question:
Has requesting priority by the "response shortcut" any reason? It just displays that the opponent wants something to do and it is only depending on me if I allow him to play at that time... Is that correct?

It helps a bit to play correctly, however some situations are pretty ridiculous, because this is not a rule in standard way.