I was wondering what whould be the best way to output video framerate at 23.976p?
That is,
#1. Is it better to shoot at 29.97 interlace, and then converts to 23.976p using cinefrom.
#2. Is it better to shoot at 25fps interlace (50i), and then converts to 23.976p using cineform.

#2 wins no matter who's tools you use.

Even with that pulldown technique thing?

That only applies if you have pulldown, a 24p recording stored in 60i -- then that is best.

I thought if you recording at 24p on the camera, then during capture we use 24p (23.976p) preset then we end-up with a 24p footage already. Is this false?

Is this something that we can check if our footage has pulldown or not? Is there a way to do so?

In the case of recording video on 5Dmk2, which is 30p (not 29.97p), and we use HDLink to go to 23.976p, is the audio will be slowed down acoordingly? The audio pitch will be way off.

Your original question only asked about 60i and 50i sources. I assumed if your camera shot 24p you would have mentioned it. 24p sources stored in 60i have pulldown. Then absolutely you should use the pulldown removal to extract the true 24p (23.976) frames from within the 60i wrapper.

If you are shooting 30/29.97p you can add a 20% slowdown with audio pitch correction.