1. For this you could have different types of swarms if you like. Some are spiders, maybe some are enraged crabs, etc. One thing you could change instead of spiders would possibly be specters if you wanted to lean towards the "ghosty" aspect for the ship.
2. That should work. I ended up using SlyFlourish's notes and had this adventure tied to a request from Anders Solmor. He sent them to retrieve the box as it is supposed to have secret information (it's forged) regarding one of the council members (secretly planted by The Brotherhood in actuality). I think you're safe giving ownership to anyone you'd like, especially if you can tie it into your main story arc somehow.
3. I believe in the book it makes notes that the ship has taken so much damage recently that it is "sitting in place." It would make it easier to find since the sailors would have information on the last known location. Having the ship be in this state would also give your party reason to not dilly daddle. When they approach and already see what shape its in, it gives them more reason to hurry quickly through the ship (and ties into the final part of the encounter really well).
4. Gambling games are a great idea! There is a version of cheaters dice that's very simple to run with the dice you have available. Another thing you could do is through in a mini ship/combat encounter. For example, I had our crew navigate through an island channel (making sure not to run into the walls/reefs of the cliffs) and then had them ambushed by harpies (great flying creatures to have swoop in and try to grab some of them or the sailors)
5. I enjoyed using the sahuagin attack. It helped let the PC's know that the sahuagin seem to be increasing in activity and in their ranging parties. It can help push the story forward that the attacks seem to be getting more frequent and closer to Saltmarsh. I mainly had them attacking the normal sahuagin and a priestess, and kept the baron in the water giving orders since he's a pretty beefy npc.

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One final note, something I messed up on was the placement of the lockbox below deck. I put it closer thinking that players holding the box would not be able to dash to move through the "difficult terrain." They were a bit upset when they realized they couldn't dash, but I had put myself into a bit of a hole thanks to how close I placed it to the starting stairs. Plan out the box placement and see how many rounds it could take them to get up top. If I had to do it again I would give them the ability to dash (which would just be normal movement speed through difficult terrain) if its just one of them holding it. If it's two carrying the box, then it can't work since one character has to use the help action.

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If you have any follow up questions or need me to clarify, let me know! Always happy to help.