I am about to enter the pit on Burial Isle, which I think is the beginning of the end game of Pillars of Eternity. To install the White March Expansion, should I do it before I start the end game or after or does it matter?

As i remember I first finished the game, then bought whitey march and installed it and continued the game. but you can install it in advance, if you already have whitey march.

I'm not really sure, but I exhausted all content that wasn't the megadungeon or what was telegraphed as the point of no return before reading off to White March. The higher level cap and better loot ended up helping me gain a foothold on the last few levels of the megadungeon. The final plot dungeon was beyond easy and the final boss went down like a chump. YMMV.

It doesn't matter - you can install The White March Part 1 & Part 2 before or after you go down to Sun in Shadow. Once you did there's no way back to the surface in any case. Just make sure to wrap up everything, including The White March questline before descending to Sun in Shadow and you're good.

isn't there even a [PROCEED? Y/N] popup that warns you? I can't recall. I know New Vegas does that.

Afaik, no.
And there doesn't need to be one, since it's made crystal clear that descending to Sun in Shadow is very much a point of no return-situation.