Adobe PDF reader and Photoshop elements 15 won't open!

As already mentioned, Apple made changes that make old programs not work... but some steps to try

-https://www.businessinsider.com/apple-macos-mojave-apps-compability-fix-2018-10

-https://www.macworld.co.uk/how-to/mac-software/open-apps-wont-work-mojave-photoshop-3684425/

-https://helpx.adobe.com/x-productkb/global/install-or-run-applications-new.html

Acrobat Reader shouldn't ask for a serial number, and should work in Mojave. Be very sure only to download the official Adobe app, or you could get malware.  What happens when you try to run Reader? Please give full details.

This is not Adobe tech support but a user-to-user forum.

I think PS Elements 15 was built to run on El Capitan.

Photoshop Elements system requirements

You could ask in the PS Elements forum  if anyone there has had luck running it on latest Mojave.  I kind of doubt it though.  Apple has made a lot of significant changes to their OS.

Photoshop Elements Forum

mojave's not compatible with pse 15 so i'm not sure you can fix that problem but you can try resetting your preferences -

https://helpx.adobe.com/photoshop-elements/kb/preference-file-locations-photoshop-elements.html, 

for adobe reader you should download and install the latest version, Adobe Acrobat Reader DC Install for all versions