Your 1st example is an improvisation.
With improvisation, how does one tell if a note is 'wrong'?
You ask 'is it o.k. to hit a wrong note?'
I counter with 'what constitutes a wrong note?'
If one is playing something like a classical piece from the dots, and trying to re-create it exactly, then yes, it's wrong.
If one is playing most other sorts of music, and happens to hit a completely out-of-key note, yes, it's wrong.
If one is playing most other sorts of music, and happens to hit a note which works - how does anyone know whether in fact it actually was a 'wrong note'?
music.stackexchange.com/users/2808/Tim
Wrong notes are never "okay".
Even as a total beginner it's very important to try to play all the right notes
so you're ingraining the right ones into your fingers and your brain.
Professionals of course try to reduce wrong notes to almost zero, but absolute perfection is almost unobtainable.
If you are improvising, it's a different story: there are no 'wrong' notes, only good or bad choices, but you should still try to avoid choosing 'bad' notes.
music.stackexchange.com/users/40545/PiedPiper
At orchestral concerts mistakes are rare.
That's 80 musicians playing at least 90 minutes of music without a mistake.
You can't have an off day.
But an occasional wrong note from the soloist in a fast movement of a concerto is accepted, as long as his/her performance is exciting.
Orchestral musicians prefer a principal French horn who plays freely and dangerously, even if that means an occasional split note.
When a jazz musician is improvising and hits a wrong note they can often cover their tracks by embracing that note and convincing you
they meant to do that.
This trick is unavailable to classical musicians.
Feel is valued over accuracy.
And that's also true of folk musicians, though folk audiences aren't even that bothered about feel!
In standard pop music, the stuff's so goddam easy to play there
really shouldn't be any wrong notes.
music.stackexchange.com/users/63087/Old Brixtonian
You should aim to play all notes correctly.
This is not everything, but it is important.
If you miss notes often, practice slower.
It pays off.
Professionals circumvent situations in which they play wrong notes.
They even practice for this.
This is a second stage.
music.stackexchange.com/users/64288/Andre
Could it be you mean e.g. someone plays Imagine by John Lennon and instead of
the triad ge-c
he adds a d?
This wouldn’t mean that he plays a wrong note!
The d is the 9th in the tonic chord ceg and gives an additional color to the music, but in the ear of a beginner it might sound weird.
There’s a typical honky tonk piano style to add chromatic approaches (#9 with the 3rd=10) in jazz and blues but also in modern classic compositions like Prokofiev’ Peter and the Wulf or Bernsteins Westside Story (Ouverture, Sgt.
Krupky, The Rumble).
P.S.
I haven’t listen to your examples.
But it could be that this is a wanted effect.
music.stackexchange.com/users/56219/Albrecht Hügli
As a beginner, I try to do my best to play exactly the notes as in the sheet music but sometimes I see some professionals hit accidentally some notes, two examples:  The wrong note was D when he wanted the C with left hand (the notes in the video are shifted by one note to the right):    Or here when he hits the C# the second time with the left hand:    My questions are how a professional can hit wrong notes frequently and is it okay?
Is it okay to hit wrong notes?
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music.stackexchange.com/questions/103673
music.stackexchange.com/users/66246/Ja_cpp
Professionals of course try to reduce wrong notes to almost zero, but absolute perfection is almost unobtainable.  At orchestral concerts mistakes are rare. If improvising, there are no 'wrong' notes, only good or bad choices.
At orchestral concerts, mistakes are rare, so musicians should aim to play all notes correctly. If improvising, there are no 'wrong' notes, only good or bad choices, but you should still try to avoid choosing 'bad' notes. Professionals try to reduce wrong notes to almost zero, but absolute perfection is almost unobtainable.