You can always do a reset and possibly it will help with whatever problem you have. As far as i know the firmware will be unchanged. Some of the Omen gaming PCs have a switch or button to restore the original factory BIOS. Those are the only HP systems I know of that can revert to an earlier BIOS without downloading anything..
What problem are you having?
Non HP ink can be used on this list of HP printers.
General ink cartridge help
I do not have an instant ink printer. My understanding is that if you run out of ink, or you cancel your subscription, you can use genuine Hewlett Packard cartridges either original or refilled. They must have an HP chip in the cartridge.
The below type is unlikely to work.
Note that this is a user to user forum and I am just the messenger of this bad news: Instant ink cartridges can only be used when the ink subscription is active.