Good video you made, very helpful. The handle is definitely the wrong one and missing parts, as you've found out. There are other things going on I could say that's wrong but they don't really matter until you source the correct handle and correct associated parts. You're doing the right thing looking at the schematics and figuring out what parts go where, next is sourcing them. Please be extremely careful with the threads, they are very precise and modifying them can effect their performance. Please double check what's needed, what the correct thing maybe needed to do and then give it some time to think about it before doing any work to them.
If you need parts, try looking at Grizzly versions of this lathe and see if yours matches up with one of there's as they sell all kinds of individual parts at very reasonable (almost silly low) prices. Jet tends to ask silly high prices for their parts.
Bummer, the PO sold you the lathe like that but maybe he didn't know any better (lets hope so). The good thing is that you are far from being alone, as paulsomlo stated earlier, there is a massive amount of these being used and customized so there's a huge pool of knowledge to pull from and a good group of people who are friendly and happy to help. You may want to check out
Paulsomlo's advice on having spare belts is also really good. Nothing is worse having your only belt go in the middle of a project. They can go fast.
I also suggest checking out Hobby Machinist Forums, a lot good info and people who are quick to reply with useful info. It's a nice place to go and learn.
EDIT: Better link to use for asking help there:
https://www.hobby-machinist.com/forums/asian-lathes-mills.451/page-2