Cannot download app, because my "MACOS cannot verify that this app is free from malware."

Try enabling the "App Store and identified developers" setting in the Security & Privacy Preference Pane:

Once enabled and the next time you try downloading Discord and see the message go back to the Security & Privacy Preference Pane. The above screen grab does not show it but you will see something once you've done these steps.

Hopefully, thereafter, it should download and install. If you've still no joy contact Discord support:

https://support.discord.com/hc/en-us

Presumably you followed Discord's installation guide?

https://support.discord.com/hc/en-us/articles/360034561191-Installation-Guide#h_22b0fdbe-12a2-499d-9b97-c0a00ae379fd

BTW how did you get on with your other problem?

Good luck.

How to open an app that hasn’t been notarized or is from an unidentified developer

Without physically looking at your laptop, no.

Perhaps it's related to your other problem? You may not have fully addressed it yet? If you haven't I would tackle that first and try again. If you don't these things will only accumulate and make your laptop less unusable.

Good luck

No I don't think so. I think something else is going on that you're not aware of or is probably related to your previous problem which, strangely when asked about, you avoid mentioning.

This is what I see when I download Discord and then launch it.

From what you've posted you don't appear to be seeing the above and yet you should be if this is a stock install and there are no other underlying issues.