1. I believe only "Wood" obtained from Pine Tree can be exchanged at a Freights(?) for wood bundles, one repairs 2000 HP over the course of time, and it goes to your Cargo (Ship inventory)
2. It's not Sashimi that restores fuel, it's Fish meat, which is obtained from Fish Swarm of Fish Swarm (Bountiful), and it goes to your Cargo (ship inventory), each restores 50 fuel per use. Additionally, you can use the manufacturing item Food Generation (price is roughly 3-4k) and each restores 650 fuel per use.
3. No, different fishing "yards" yield different types of fish, Fish Meat is obtained from the above mentioned sources only.
4. You double click it inside your Cargo (Ship inventory) to use, the Repair Skill has no use currently whatsoever.
5. You generally don't need it because once you get the hang of different sea monster's attack ranges, you can avoid most of them and take minimal damage. Your fuel should also keep you alive for around an hour till you get to a nearby Haven or Isle. However, if you plan on surviving with the wood bundles and fish meat, then yeah, that's what you need.
-Fishing needs to be lv1 for Fish Swarm and lv2 for Fish Swam (Bountiful)
-Woodcutting can be either lv1,2 to chop Pine Trees which yield low amounts of wood (Abandon mine haven area) or lv4,5 to chop Pine Trees which yield high amounts of wood (Chaldea Haven area)