To Q1:
Both are connected at one point , however the PE can (and will) carry more noise due to currents (up to 30mA or even 300mA depending one the installed RCD, in some cases even higher ) from line filters in switched power converters , C&L coupling to the line power etc..
While the PE is build (and tested! ) for low resistance the impedance (here inductivity) can be quite high, so RF content is not well grounded.
So a instrument earth as an separated path is build up, but not with the intend to carry lot of current, just to establish a clean ground potential.
To Q2: A capacitor to ground will be low impedance for high frequency (Z=1/(j*2*pi*f*C)) but not for DC . On the other hand an inductivity is a good conductor for DC , but not for AC (Z=j*2*pi*f*L).
Depending on the task you have, you can decide what part you tide to ground.
Greetings from Germany
Henrik
LV since v3.1
“ground” is a convenient fantasy
'˙˙˙˙uıɐƃɐ lɐıp puɐ °06 ǝuoɥd ɹnoʎ uɹnʇ ǝsɐǝld 'ʎɹɐuıƃɐɯı sı pǝlɐıp ǝʌɐɥ noʎ ɹǝqɯnu ǝɥʇ'