That's not precisely true. If you accidentally, or incidentally touch a piece, you don't have to move it.
FIDE rule , touch move, please help !?
They can give you all the trouble they want, but FIDE rules clearly exclude accidental touching from the touch-move rule

Article 4: The act of moving the pieces |
|
4.1 |
Each move must be played with one hand only. |
4.2.1 |
Only the player having the move may adjust one or more pieces on their squares, provided that he first expresses his intention (for example by saying “j’adoube” or “I adjust”). |
4.2.2 |
Any other physical contact with a piece, except for clearly accidental contact, shall be considered to be intent. |
4.3 |
Except as provided in Article 4.2, if the player having the move touches on the chessboard,with the intention of moving or capturing: |
4.3.1 | one or more of his own pieces, he must move the first piece touched that can be moved |
4.3.2 | one or more of his opponent’s pieces, he must capture the first piece touched that can be captured |
4.3.3 | one or more pieces of each colour, he must capture the first touched opponent’s piece with his first touched piece or, if this is illegal, move or capture the first piece touched that can be moved or captured. If it is unclear whether the player’s own piece or his opponent’s was touched first, the player’s own piece shall be considered to have been touched before his opponent’s. |
4.4 |
If a player having the move: |
4.4.1 | touches his king and a rook he must castle on that side if it is legal to do so |
4.4.2 | deliberately touches a rook and then his king he is not allowed to castle on that side on that move and the situation shall be governed by Article 4.3.1 |
4.4.3 | intending to castle, touches the king and then a rook, but castling with this rook is illegal, the player must make another legal move with his king (which may include castling with the other rook). If the king has no legal move, the player is free to make any legal move. |
4.4.4 | promotes a pawn, the choice of the piece is finalised when the piece has touched the square of promotion. |
4.5 |
If none of the pieces touched in accordance with Article 4.3 or Article 4.4 can be moved or captured, the player may make any legal move. |
4.6 |
The act of promotion may be performed in various ways: |
4.6.1 | the pawn does not have to be placed on the square of arrival, |
4.6.2 | removing the pawn and putting the new piece on the square of promotion may occur in any order. |
4.6.3 | If an opponent’s piece stands on the square of promotion, it must be captured. |
4.7 |
When, as a legal move or part of a legal move, a piece has been released on a square, it cannot be moved to another square on this move. The move is considered to have been made in the case of: |
4.7.1 | a capture, when the captured piece has been removed from the chessboard and the player, having placed his own piece on its new square, has released this capturing piece from his hand, |
4.7.2 | castling, when the player's hand has released the rook on the square previously crossed by the king. When the player has released the king from his hand, the move is not yet made, but the player no longer has the right to make any move other than castling on that side, if this is legal. If castling on this side is illegal, the player must make another legal move with his king (which may include castling with the other rook). If the king has no legal move, the player is free to make any legal move. |
4.7.3 | promotion, when the player's hand has released the new piece on the square of promotion and the pawn has been removed from the board. |
4.8 |
A player forfeits his right to claim against his opponent’s violation of Articles 4.1 – 4.7 once the player touches a piece with the intention of moving or capturing it. |
4.9 |
If a player is unable to move the pieces, an assistant, who shall be acceptable to the arbiter, may be provided by the player to perform this operation. |

A lot of the above describes what SHOULD happen but as far as I know, Assuming there are no witnesses and no arbiter assigned to the individual game, and the person wasn’t well known for such things, and it was one persons word against another, the ‘touching’ player would get the benefit of the doubt.
You could certainly stop the clock and make the arbiter aware of your version of events but if the opponent refused to admit it there probably wouldn’t be anything you could do on the first occasion.
"if the opponent refused to admit it there probably wouldn’t be anything you could do on the first occasion. "
Too true, although I'm happy to say that I've never had to confront that problem. But remember, if you brush against a knight while reaching fot a bishop, you don't have to move it. Intention matters

So WHAT should opposition do in this scenario, when opponent already touched one piece, but then moved ANOTHER piece and pressed the clock.
What should you do? Call an arbiter and explain and if player admits it , is it illegal move or what?
Or without calling an arbiter just swith back you clock button, back to his time running and tell your opponent to move another pieces
What is the right behavior in this particular situation occurred?

Unless your opponent agrees to move the touched piece, calling an arbiter is the best idea.
And what if he agrees , but because he pressed your time first and it was running say 10, 15 seconds already and then he agrees that he touched another piece first , so you switch back to his initial time BUT you are already lost time because of this, so who's going to conpensate your time loss? I mean it seems little 10, 15 seconds , but what if he continues doing this ? Isn't that an Ilegal move or...
?
"Bullshit. There is no such thing as "accidental touching" in FIDE rules."
Sadly, reading comprehension is declining world-wide. Check rule 4.2.2 is post #6

They can give you all the trouble they want, but FIDE rules clearly exclude accidental touching from the touch-move rule
Bullshit. There is no such thing as "accidental touching" in FIDE rules.
I can give you the rules but I cannot read for you.
Every arbiter I know wouldn’t sanction „accidental“ touching e.g. with your sleeve.
-in the ideal case the arbiters intervene if they notice it
-there might be differences in the USCF, Nakamura has problems following touch-move.

#13
So if I tell an arbiter , then what is the correct arbiters behavior? Is it an Ilegal move or...?

Call the arbiter, describe the scenario and let him do his work. You‘ll receive a time bonus as well probably. If you and your opponent have different views and no witnesses it can become arbitrary.

What if a player touches his piece when it is opposition turn? Does the touch rule apply then? Player cannot make his move because legally it is opposition turn. Please clarify
Scenario:
Opponent touched a piece (knight) , then decided to touch bishop and move bishop instead of knight.(moves the bishop and presses the clock).
Opposition immediately notice it and.....
What is a correct behaviour after this? Pause clock and arbiter required? If yes what punishment should arbiter conclude? I mean sure he can just switch back the clock and return move back, BUT what about 5,10,15 seconds lost? Who returns time?