Some good advice in here, so I'll try not to replicate too much. But if I was running this encounter, here are my thoughts.
1) There will be attacks by creatures with harpoons (with rope attached) and pincer staff. They will want to be dragging the PC's into the water to drown them. Harpoon could just stab without the barbs engaging properly. The pincer staff could just clonk someone without actually grabbing them correctly. How would you handle the chance that the weapon actually has them?
I assume that dragging them into the water would would just be an opposed athletics check. Maybe with a penalty for slippery rocks.
Would it be with advantage or just a bonus, if 2 harpoons get the same PC?
So there are some interesting things in here. If the weapons are a special kind of harpoon, then something to consider is that your players may be able to grab them from the enemies after the encounter. So if the special abilities are tied to the weapon, you may be giving them access to whatever the enemies are doing. Whether it is a ranged grapple or restrain, or whatever. So you may want to determine how to handle that and what you are willing to potentially grant the players. If you aren't too comfortable with it, you may want it to be a special skill (maybe a feat that the enemies posses) or more of a racial ability that allows the enemies to use these harpoons in this manner.
Once you figure that out, another consideration is that encounters in 5e are usually pretty quick. On average 2-3 rounds is typical. This means that if you make the grapple/restrain ability too complicated or avoidable, it may not even happen. Not saying you should have it be automatic, but you wanna balance the cinematic action and suspense of the encounter with the heroics of your players.
I think this would be a good instance to consider Action Oriented Enemies as presented by Matt Colville. This might be a way to get your bad guys a chance to use really special and unique abilities that otherwise might not go off using tradition action economy.
2) There is likely to be a constant low level spell effect going on for a while. I don't want to hassle with constant saves every round. Is a passive will save of 10 +bonus reasonable? But then it would probably never happen or always happen. Hmm... Not sure how to handle that one. Advice?
What is the effect, specifically? Something to consider is that the DM is not bound by the same rules or mechanics as a player character. If it makes sense, you might just want to allow an initial save. Those who save are not affected, and those that fail are affected for the whole combat. Alternatively, you could require the player to use an action/bonus action/inspiration point to reroll the save on their turn. This reduces the need to remember to allow the save and puts the agency in the player's hands regarding how much they want to mitigate whatever this spell effect is.
3) Can you decide to intentionally fail a save in 5E?
Yes. The situations are rare when a player may want to choose to fail, but I allow it. One example off the top of my head is I might allow a player to use a reaction to put themselves between another player/NPC and an attack or spell. They have to volunteer to fail their save to do so. So they may take the hit for someone else.
4) PC's might try to use a longboat during a bad storm. How would you handle determining if they go the right direction and don't founder the boat? The creatures from 1) above are likely to try and capsize the boat. How should I handle that attempt?
I would make this a group skill challenge of sorts. Whoever is helming the boat would need to make a water vehicles (dexterity probably, but intelligence or wisdom could make sense, or even constitution depending on how physically taxing it is to keep the boat from capsizing) check to maintain course and keep the boat steady (I would allow this to be untrained if no one is proficient in water vehicles). They or another player would make a survival check to keep the boat on a specific course or direction. This I would probably require the player to be trained in, unless no party member is trained. Then you ask the other players how they are assisting with the boat and base the challenge on that. If they are actively fighting the enemies from 1, handle it like combat. If they are doing things that aren't quite within the bounds of what typical combat looks like, I would just let them take actions and figure out an appropriate check.
One thing that will really help this is by having degrees of success/failure. If the fail a check, but only by 3-5 (your choice depending on the difficulty of the task), allow the action to succeed but with some kind of complication. If they succeed by more than 3-5, have them succeed in a way that is even better than expected. And if they crit succeed or fail, that is when the real fun begins. This allows for more variety in the outcomes, but also ensures that they are generally heading towards a decent outcome. Of course, you can certainly reverse how you're handling the degrees of success/failure to make it harder.
5) Does 5E have creatures that eat or otherwise destroy magic items?
A rust monster could destroy a magic item by eating it. But 5e is generally less punishing on players, so there are fewer abilities or monsters that destroy magic items than in previous editions. You can probably mine monsters or spell effects from 3e/3.5 that could be adapted for use in 5e.
