This looks like tar, which would have to come from far away tarpits.

That was my first thought, and my second was that such is maybe just a trope.

Faraway tarpits means effort, expense, and inconvenience. Plant-sap pitch might be more likely as something with a double-use for sealing various castle cracks (wood, stone).

There's also the fact that pouring boiling tar or pitch would be difficult all the way around-- to heat as necessary, pour, and later to clean up. Whereas oil would be easier all-around, methinks. And much better if it could be locally-sourced.

Lead wouldn't ignite if some dripped on the outside of the container it was in. You could also move it separately from the container and just refill the container after each pour.

Depends on how they store it and who's willing to handle it, I suppose. It was pretty common in castles to dedicate one wall to the latrines, which would protrude outwards over the wall, with the holes having no bottoms. So #1 and #2 would just drop and collect next to the wall, outside the castle. Before an impending siege or whatnot, you could maybe have people go down there, collect the leavings, and haul it up top to dump on the invaders.

In reality, I'm guessing that a mix of substances were probably used depending on place and circumstance. Just emptying the nights collection of chamber pots would work, which is probably what you were thinking of, right?