I have run it on 5 computers with Win10, so Paintshop Pro 7 will work, but there are a few quirks with it...
You could optionally choose to run it in compatibility mode, but that will only fix one issue, and introduce another. I choose not to run it in compatibility mode, as it prevents one from being able to make screenshots of the program UI.
First, you will see an error message that looks something like this, each time you run it. It happens once or twice, as soon as the program launches. Just dismiss them and proceed on to using the app. This has been an issue with PSP7, since WinXP. You might also see one when you try to close it. Same thing...ignore and close the messages. Running it in compatibility mode will get rid of the error messages, but you'll still have to click away a prompt to allow changes to your computer, every time you run it. So, all you'd be doing is trading one type of message to click away, for another.
The 2nd, more annoying quirk relates to the small pop-up windows for tool options, layer palette, overview, etc. Win10 won't show you the rollup buttons that should be on them, but they are still there, invisible. so you have to click next to the close (X) button to lock open or rollup, as shown on this screenshot.Paint Shop Pro 7
Otherwise, I'd recommend setting automatic rollup in preferences:
The 3rd, most annoying quirk is related to 3rd party filters and plugins. Some of them that used to work well under other versions of Windows, will not work on Win10, and there's nothing you can do about it, since all of them are no longer supported by their developers, and rarely would they ever offer any help to Paintshop Pro users even when they did support them, as they were written for use with old, outdated versions of Photoshop, not Paintshop Pro.
Other than that, it works perfectly fine and is still my favorite image editor.