I have case, or two actually. There is a warrior fraction card (don't remember the name atm) that has an immediate impact and says 'Your opponents have to pay 2 pearls to the bank'. If you have just one pearl or none, the case is obvious, but when you have a pearl and a couple of black ones, can you pay the cost with one pearl and one Nebulis?
I would say the answer to this is no. In the rule book it mentions on the top of the 4th page pretty specifically when you can use them. I'm not going to quote it exactly but its very clear that you can only spend a nebulis when buying an ally that an opponent offers you on their turn, or when using pearls to help you complete the sum of the cost for a Lord. There's also a note on the page labeled "important" that says a nebulis cannot be used to plot at the court. This seems to reinforce that the only time you can use these nebulis is in the two situations I stated above (and there are Lord effects that let you spend them as well but they say on the cards themselves).
The second question. When someone gains two or more black pearls, and one of the players have an active lord card that allows him to gain a pearl each time an opponent gets two pearl or more, does it count?
I don't have a reference for this but I would say no, you do not get a pearl if your opponent takes a nebulis. My reason is that throughout Abyss and Kraken, it's made very clear that pearls and nebulis are different resources. Nebulis can normally be obtained through the kraken cards. I highly doubt that a Lord's power would let you gain a pearl for someone obtaining a nebulis. If I were playing the game I would rule this as NO but of course, an official ruling is always welcome