They aren't mutually exclusive.
Can U really Win a Chess Game ?

By definition, a game with no mistakes by either player is a draw... So yes, you cannot "win" against perfect play.

Not technically true you can win on time
That's also a mistake by your opponent!
It's not a 'weak move' though. Unless your move strength factors in time too.

Absolutely. Using all your game timer for one move is a very weak move, isn't it?
How about half of the timer?
And so on.

The notion of it not being a win just because your opponent didn't play perfectly is plainly nonsense anyway.

Almost all games ever played in chess history have been containing some or the other mistakes
Of course. Thankfully we aren't all computers, and no CS major (like I will be) has solved chess yet.

The notion of it not being a win just because your opponent didn't play perfectly is plainly nonsense anyway.
Bingo.

Well... chess hasn't been solved, so define mistakes. If I play white and checkmate someone using the Fool's mate or the four-move checkmate, I did not make a mistake.
In fools mate, its white who looses, not black
Fools mate first move is either 1.g4 or 1.f3, not 1.e4
It's been my experience that "wins" are the result of weak moves by your opponent. Sooo you don't win. Your opponent looses.