Does beg the question why the Jackdaw was back in the Caribbean when Edward took her to England. So either he did go back to deal with Rogers in 1732 or he gave the Jackdaw to the Assassins or potentially to someone else. Possible he just sold her but chances are he gave her to the Assassins. So potentially the Jackdaw was the first of the Assassin fleet and was later joined by the Aquila ... but the two didn't last together very long before the Jackdaw sank. Aquila was built in the 1730s would would likely be around the time the Jackdaw went down. Unless the Aquila was built to actually replace the Jackdaw.
Makes you hope Ubisoft fills in that hole, but can't say I'm counting on it. Given how long some of us have been pestering them regarding Connor's fate and we've gotten nothing but a hand slap and given dangling keys to distract us, not betting on the Jackdaw's end being explained. Would be rather random for it to pop up in the next game or the one after without a good reason. Altair's fate in Revelations made sense, but put Ezio's fate in AC3 and that would've come out of no where. I'd bet Initiates will likely be the only way they'd reveal what happened to the Jackdaw (and potentially other loose threads) since that's just little blips of information attached to dates. Doesn't require anything massive for them to work on besides maybe a picture and a paragraph or two.
1.) Jackdaw sank northwest of Jamaica suggesting the ship was possibly heading to Kingston or just left Kingston.
2.) Jackdaw's about 50 miles or so off the coast of Jamaica.
3.) Jackdaw was damaged enough to lose the figurehead off her bow and (if I saw it right in the video ) was lying in 2 pieces at the bottom of the sea floor.
1.) Edward went to the Caribbean to kill Rogers in Nassau and possibly brought the family making the excuse of it being a family vacation. He could then use them as an aliby and an excuse to get out of some situations. Judging from the AC4 ending, Haytham wasn't beyond pestering his father for something even when he was in the middle of a conversation. While sailing back to Kingston to meet up with Tessa, Jenny, and Haytham after killing Rogers in Nassau, he got caught by enemy ships (Templars, pirate hunters, etc). Edward decided to make the enemies think he was dead so abandoned ship and blew up the Jackdaw. A nearby ship then picked him up and took him back to Kingston.
* Since we're not sure how long Jenny knew Edward was an Assassin, possible she could've found out around this time or possibly just before. She found out at some point before 1735 and knew a hell of a lot longer than Haytham did.
**Apparently in the book, Rogers got kicked out of the Templars after he returned to England. So either he somehow got back into the Order or Edward just killed him to complete his promise to the Assassins.
2.) Edward gave the ship to the Assassins who then took it to the Caribbean to deal with Rogers. Ship got caught in a naval battle and lost due to an inexperienced crew.
Alternate option: Jackdaw got caught in a hurricane or water spout and went down. Also possible a spark got into the gunpowder and up went the ship.