No offense but there are prior discussions claiming to solve this one in regards to the printer driver.
Without me looking at priors I usually look to HP and see if they have a W8 driver. That usually works.
https://support.hp.com/us-en/drivers/selfservice/hp-color-laserjet-1600-printer/1140734
As to the XP to W10 share not only is the basic items to deal with but we must be very aware of router firewalls. These can be one way as I noted in the CNET Networking forum sticky about Samsung Owners, start here.
Since we know that, I won't duplicate that here and share my research from here on:
https://support.hp.com/us-en/drivers/selfservice/hp-color-laserjet-1600-printer/1140734
I see W8 64 drivers.
As to the XP share, the router firewall SHALL be disabled until we get this working.
https://helpdeskgeek.com/how-to/xp-to-windows-7-8-10-printer-sharing/ and many other posts are out there.
Upgrading - Have a Windows 10 machine hardwired to an XP machine. Have it mostly working, but have two problems. 10 machine can see xp with no problems, but xp cannot connect to 10. Workgroups are the same. I can see it but cannot access. Obviously problem is security. Tried everything I could think of to no avail. Also, I have an HP Color Laserjet 1600 on the xp machine. It would seem that HP did not deem to make a driver for it for 10. Anybody know of a driver that will work so I can use it on the network?

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