Can you add a photo or photos of the accessories? Do that and we can soon identify them between us, for you.
As a start:
The chuck that is on there, looks to be the 3-jaw variety. That T-shaped item in the tray below it, is it operating-key.
A four-jaw chuck is similar but, well, with 4 moving jaws.
A faceplate is a large disc with a threaded hole in the centre, and a pattern of several radial slots or holes. Like the chucks, it is for holding work-pieces.
The "change-gears" Howard cites (aka change-wheels) are a set of gears each with the number of its teeth stamped or embossed on it. They are assembled by their appropriate numbers onto the lathe for when cutting screw-threads.
The pointed thing sticking out of the "tailstock" (the tall, red unit at the right-hand end), is a "centre" and there should be at least another, with a sharp point at one end and a longer, tapered tail (that in the photo is hidden inside the tailstock).
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So, if you can supply photos of whatever there is with this machine, we can identify at least the most important items, and possibly weed out any odds and ends that have moved in with them. Doing that will enable you to catalogue it properly and hopefully find a caring new home for it all.