What direction does 0° in the J2000 epoch point towards on January 1, 2000? Is 0 degrees in the J2000 Epoch 'right ascension' is a line from Earth to the sun on January 1, 2000? Or is 0 degrees the direction towards the ascending node 'equinox'?  Which is NOT towards the Sun on January first...
Or is 0 degrees the direction towards the ascending node 'equinox'? Which is NOT towards the Sun on January first...

The answer is yes, more or less. From JPL's HORIZONS, the location of the Sun at Noon Terrestrial Time on 1 Jan 2000 is, ignoring atmospheric effects, a right ascension of 18 hours, 45 minutes, and 9.36 seconds. This is nowhere close to a right ascension of zero hours (or 24 hours, same thing).
The right ascension of the Sun with respect to the center of the Earth is zero at the March equinox.