Do the members of the small council (Master of Ships, Laws, Coin, Hand of the King, etc) draw a salary? Or maybe get some kind of break on taxes owed? Or does having such political influence make payment unnecessary?

I could have sworn I wrote about this before, but can’t find where I wrote it, so at the risk of repeating myself, I’ll do it again.

Yes, they probably get a salary, but probably not a large one in part because the Small Councilors are supposed to be noblemen who live off the incomes of their lands.  

If Westeros is like Medieval and Early-Modern England to any extent (and since GRRM is largely drawing from English history here it probably is), then there are salaries that come from working for the monarch, either in the private household or the government itself.

For example, Queen Elizabeth I’s laundress got paid 

£4 annually, plus another 

£6 to pay for livery (i.e, clothing with the queen’s sigil, her required uniform). Her Lord Keeper of the Great Seal, a high-ranking Privy Councilor charged with keeping the seal of England, got paid 

£919 pounds annually, and that was pretty good for the time.  

At the time, however, there was also a form of socially accepted bribery and kickbacks. As Lacey Baldwin Smith points out in The Elizabethan World:

“…no Elizabethan official ever received a salary that was commensurate with his position: the Lord Keeper of the Great Seal earned a stipend of 919 pounds a year; the Lord Admiral 200 pounds, and the principal secretary 100 pounds, but in 1601 all three posts were actually valued at approximately 3,000 pounds a year. Gratuities and fees for promoting a friend, urging a favor, giving information, and above all, for tapping and directing the bounty of the queen made up the difference…they were considered the legitimate perquisites of office in an age that regarded governmental posts as both public trusts and private sinecures.”

So chances are that the Master of Laws gets gratuities from people seeking to have their cases heard by the King, the Master of Ships from merchants or shipbuilders looking for business, etc. However, as we see with the case of Littlefinger and Janos Slynt, there are informal norms about what’s ok to do and what isn’t – Stannis recognizes that bribes happen, but treats selling officer positions in the Gold Cloaks as unacceptable; Littlefinger putting his own men in office is normal, but using public funds as his own investment bank is not.