They seem to be just a couple of "yes-men"(or yes-people).
They hardly say anything informative apart from the blatantly obvious and appear to watch "Lord Sugar lumps" to see his reaction so they can say what they think he wishes them to say.

I think they inform LS before the boardroom takes place. How could he know all the details otherwise?

No idea.
If only someone were filming it...

LS doesn't watch the footage - he totally goes on what Nick and Karren tell him.

Source please?

I'm not so sure anymore.

There's probably around 40-60 hours of footage per task. He can't watch it all, and the show runs at far too fast a clip for people to produce a sufficient edit in time to show him the relevant parts. He may well get pointers from production staff as well as Nick/Karren, if we're being cynical, but he can't watch the footage, except maybe for a few critical points like pitches.