I know it’s on the Selbina ship. I really want to fish for nebimonites. What lvl should I get before I fish on the ship? Any advice fishing for them and staying safe?

Generally the fish skill levels on Nas are the same as retail. FFXIcyclopedia says that the skill cap for Nebimonite is 27 and you can usually catch fish with a skill as low as 20 levels below the cap, which means that by level 7 you can catch them and I'd probably say that by level 9-10 you can catch them reliably. Use a composite rod, on Nas it's good for virtually everything (maybe except legendary fish).
The ship is buggy on Nas, which can be lethal - Some times mobs that should only appear on the ship deck (either pirates or fished up) appear below deck and/or can see and aggro through the deck, which means that until the bugs are fixed you can't just hide below deck if there's trouble. Another serious bug is that sometimes there are two "instances" of the ship, one with pirates and one without, with players being randomly split between them, which also means that you can't board as a party and assume you're safe because there's a chance that some of you will get separate from the others.
Worst case scenario (albeit chances are small) - You get separated from everyone else due to the bug, ending as the sole player on the ship with pirates and you're unlucky enough to get not only the regular pirates but also the NM and due to the second bug it spawns below deck or aggros you through the deck, you'll end-up dead even at level 70. With that being said, if you board with other high level players the chances of all of these things happening at once is small and around level 50 all mobs except the NM will be TW and won't aggro anyway so you can just ignore them and fish. Last time I ran into pirates I was RDM45 and still got aggro but only from a single Ship Wight (Crossbones did not aggro) and it was easily soloable.
With that being said the only way to be truly risk free is switch to a level 1 job before boarding (there are Nomad Moogles in both Selbina and Mhaura) so you don't have any exp to lose if you die. I'd say that chances of having any mobs on board are around 25%, usually the ride will be monster-free (except for fished-up mobs, which only aggro whoever fished them up).
Don't fish-up monsters on board the ship - You should be able to handle them around level ~35ish but it'll take you longer than the 30 seconds it takes for the fishing minigame to time out.

Good luck.

Adding to Nightcoder's excellent advice, if you are a level 20 RDM or WHM you can Sneak yourself while you fish (the buff isn't removed by fishing). You still need to survive the first few seconds of transitioning on the ship's zone without aggroing anything through the ceiling. If there are high-level players with you, use of Scroll of Reraise before a ship leaves the port (you can then accept the resurrection after they clean the deck, otherwise don't bother) and make sure you have full HP (blood aggro...).

_________________
Baleful Badger

Very accurate, just further clarifying -

• When the ship leaves port it's considered zoning therefore it removes Sneak and Invisible (not sure invisible is needed though), that's why you need to survive the first few seconds without aggro (at least until you can sneak yourself again - very recommended to macro it to save another few precious seconds). All other buffs remain though, that's how I managed to easily get rid of the wight that did aggro me last time.
• Someone I talked to tried to stay dead until the ship arrives at the destination and told me that apparently the ship never arrived. Possibly the ship cannot arrive as long as there's someone dead on board so can't be 100% certain. If there are mages that can Raise you they are most likely to do so, otherwise please be considerate if people ask you politely to HP. Note that even if you're raised you still lose exp, that's why I still recommend switching to a level 1 job.
• Skeletons and wights that aggro by HP (as well as hearing) aggro (if I remember correctly) by the percentage of HP you have left, not by the absolute number of HP. This means that if you're raised and immediately cast cure so you have full HP you wont get aggrod (and assuming you re-sneak as well), however when your weakness wears off then the same number of HP now becomes a low percentage and you will get aggro so make sure you hit that Cure III immediately.
• Actually that last bullet is pretty worthless - as Piellar said you should probably only bother raising if other players have already cleared the deck.
• Oh, one thing that can really help you - If you really need to tell something to other players on board (e.g. please clear those mobs that are TW for you but still IT for me) one trick is that you can still send messages to your LS when dead - just ask one of them to /tell one of the people next to you.

Follow Piellar advice!

Did the bug get fixed where letting it time out freezes the game? If not, don't bother fishing until you can kill the monsters; even sneaking isn't worth it because they won't despawn when the ship lands at port, and will kill you through the floor next time you zone in.



I believe this is just a random personal bug that can occur whether you are dead or alive.



You will likely be in blood aggro range and get aggro before you are able to cure yourself. Follow Nightcoder's next bullet and stay dead.



You can still send /tells while dead. And talk in party chat. You just can't use say/shout(/yell?).

Weird that I remember that I couldn't /tell when dead, maybe I'm mistaken.
Regarding the HP aggro, may not properly apply here but generally it is a good idea to mind that when raised & cured you can actually attract aggro when the weakness wears of if not immediately cured again.