2) The efficiency of raid coasts is based off of the trade node's pirate efficiency, so the general advice is to use the Hunt Pirates mission. Not sure if you didn't know that or if you're saying that it's changed.
Yes, but since them raiding you gives you free 100% effective protection for [cooldown] years, and since your fleet only has interrupt its "pretend to hunt pirates" mission for a couple of months for them to raid you, doing "pretend to hunt pirates" is pretty much a waste of time and resources. I haven't actually done the math on the cost of dedicating a substantial fraction of your naval capacity to doing nothing except "hunt pirates", ever, but I doubt that it's much less than the cost of being raided, especially when you figure in the opportunity cost of not using a large part of your fleet for fighting wars or "protecting trade [during peacetime]" which is apparently something completely different from "hunting pirates". And if your "pretend to hunt pirates" fails however briefly for whatever reason you might as well not have bothered doing anything at all.
It's poor, half-finished, game design. This is supposedly a "strategy game" with "interesting decisions", but from the raider's point of view it's free money for pressing a button - hardly an
interesting decision - and from the raidee's point of view you're probably better off just taking the raid rather than trying to protect against it (but, hey, there's that
interesting micro-management of making a note of when the cooldown from the last pirate raid expires so you can start your ships on the protection mission the month before the timer expires). The raider has no chance of direct consequences. Ships "hunting pirates" never actually do anything to pirates. Being raided gives you no casus belli, even though historically such raids led to their share of counter-raids, and even though when other nations that pirate you (far less effectively) you get a CB. In a game where something as trivial as "diplomatic insults" gives you CB's that the game nags you and nags you and nags you about not using, this action that actually harms you gives you no diplomatic response. Also, an AI will raid countries which the UI says it has a "friendly" attitude towards, which is really bad strategy if the AI actually wants to have a friendly relationship with the country it's raiding (which presumably it does), and which makes diplomacy a useless strategy for this purpose.
If there was a chance of ships doing a pirate hunting mission costing a pirate raid some ships, that would make pirate raids a more interesting decision. If raids gave the raided countries a CB, perhaps one of those CB's that I've never had occasion to use like "cb_privateers", that would make pirate raids more interesting. If diplomacy that persuaded a country to have a "friendly" attitude towards you would make them stop raiding you, that would make it more interesting. If it were multiplayer, the player considering raiding me would have to think about diplomatic consequences, which might make it interesting depending on the context.
But as it is, there's no strategy to it and no interesting game play. It's just a "free money" button that some countries get to push, and which is really frustrating to be on the receiving end of because there's nothing cost-effective you can do about it.