Solved: https://i.postimg.cc/zv5SSTwn/psp01.jpg
(all three/four technical questions, pending persistence after reboot)

Based on information posted today in alt.comp.freeware...

1. The latest known-good version of PSP is, most likely, version 5.01
http://www.oldversion.com/windows/download/paint-shop-pro-5-01
Name: 5.01_psp501.exe
Size: 18241961 bytes (17 MiB)
SHA256: 7D3ED18F0A6CF25C8F09F5241CA73A6E40599569ABEBFA3F1D BCCED614B058EB

Name: psp.exe
Size: 3632128 bytes (3547 KiB)
SHA256: 42CAB30E7F657C8B8C686F7305CE5C61D111992C04CCA3BED9 8DDB14BD7DCBC8

2. I disabled the PSP errant Recycle Bin context menu
Using Nirsoft "Shell Menu View" freeware
[HKCR\Folder\shell\Browse with Paint Shop Pro\command]

3. I disabled the PSP errant "New" menu with Nirsoft "Shell Menu New"
[HKCR\.psp\ShellNew]

4. I created a new custom context menu for editing "psp" files using
Default Programs Editor http://defaultprogramseditor.com/

In summary, psp version 5.01 is apparently successfully installed:
a. INSTALLER === x:\app\editor\pic\psp\{5.01_psp501.exe,syslog.log}
b. INSTALLED === c:\app\editor\pic\psp\psp.exe
c. SHORTCUT === c:\menu\editor\pic\psp\psp.lnk
d. MENU === Taskbar menu editor pic psp
e. APPPATH === [HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\App Paths]
f. COMMAND === Win+R psp
https://i.postimg.cc/zv5SSTwn/psp01.jpg
--
The high expense of freeware is learning how to deal with its quirks.