One thing about these that can come as a surprise is that they fit perfectly in any case or gigbag made for a telecaster. I have a peardrop-shaped hard case that I use for my telecasters, but it also fits my danelectro longhorn like a glove.
From what I can see in the pics that have been posted, I would say that the body does go with the neck. In particular the shape of the control cavity is familiar.
From the pics it certainly looks identical to the 1990 japanese '62 reissue Precision I used to own. I can't see the strap buttons clearly, but it looks like they might have been swapped out for staplock buttons. I recall there was also a 'hootenanny' strap button on the back of the headstock. It also looks like someone took a dislike to the finish on the back of the neck on yours for some reason.
I'm a big fan of my H2n, and use it to record every rehearsal and gig. I will probably wait for the next iteration of the h2 before thinking of upgrading, but the 32 bit float, usb-c, and bluetooth control look like worthwhile updates.
I have a blueburst one of these, its a great bass that I'd be using a lot more were it not for my three JMJ Mustangs.
There's no need to replace the tuners — I use LaBella's danelectro-specific set of flatwounds and they are perfect.
https://www.bassdirect.co.uk/product/la-bella-760-fd-dan-electro-stainless-flats/