>>> Should I still be able to use Elements 13?
Yes, your Elements 13 can still be used, but only on earlier operating systems. Not, unfortunately, on macOS Catalina for technical reasons due to Apple, not Adobe.
Versions of Elements earlier than the current 2020 include 32 bit components which can only run on Mojave or earlier. Apple dropped support for all 32 bit software in Catalina, which renders all 32 bit software unusable on Catalina - that includes Elements 13.
Your options:
- Upgrade to Elements 2020 and use that on Catalina, or
- Downgrade your computer to Mojave and install Elements 13, or
- Use a different computer for Elements 13