I would suggest the "poles " with pulleys are parts of a milling-spindle, typically for wheel-cutting on a horological lathe, especially as the spindle clearly carries a dividing-plate.
As well as more complete replies here, try looking at other examples of similar machines (e.g. on the lathes.co site), and seeing what fits convincingly together, to help sort actual lathe parts from lathe accessories from odd bits that hitched a lift with it.
A " round knurled ring with grub-screws" could be a simple adjustable stop or a knob for rotating a spindle somewhere.
If the "top slide " isn't that, might it be a vertical slide? You describe the second purchase as a collection of parts, so it could be a top slide but from some third, unknown lathe. Possibly collected by the seller who thought he could adapt it for Something Very Useful
I have found old machine-tools seem to lose important or useful bits, but attract mystery bits to sit there and defy you to identify them!