H&R Block software won't install

I bought the usual H&R Block download at Office Depot. When I try to open it after clicking on the dmg file and dragging it into Applications, I get the message "You can't open the application 'H&R Block 2020' because it is not responding." I have this same issue with anything I download that is not Mac software: the HP fix for the infamous "HPDevice Monitoring.framework" will damage your computer" message, to apps when I want to screenshare with tech support at various places: anything. Permissions are in order and Disk First Aid turns up nothing. Is there anything I can do that is not draconian? One fix I read required reinstalling the OS, which I don't want to do. I use a MacBook Air early 2015 running Catalina. Thanks.