What is that weird sound? breathing?

in the first it might be the bow strings ...

in the second I was too annoyed at the over-dramatic pianist loving herself like she is some kind of goddess or something for being able to play a song someone else wrote [try writing your own song] I never got to whatever you were talking about. if it sounded like crying, it was probably the ghost of Bach.

The 1 st one (cello) is the fabric or material from his sleeves rubbing.

The second is a vibration, probably from the microphone they usually put inside the piano when it's a grand piano like that. It is probably the pedestal vibrating or the microphone is too close to the edge and knocking against the side, still, a vibration.

In the first extract it is indeed the gamba player BREATHING (can you see his sleeves rubbing? no!). This is sadly an all too common fault with badly-disciplined players who use breathing to 'count-out' phrasing etc. I have heard much worse than this and it can be very distracting. Please for musicians PLEASE DON'T HEAVY-BREATHE AND SNORT!

The second one is the same - invasive heavy breathing. You can actually SEE her taking the breaths and catching the occasional fly if you watch carefully.

Bad habits!

In the cello, I think your hearing the bow hairs actually moving across the strings. On the piano,

I think you're just hearing overtones that are tricking your ears.