Do manually installed programs/packages get updates automatically?
I downloaded android studio as a .tar.gz into home directory on ubuntu 20.04 and then I discovered that downloaded software is conventionally put in /opt directory. So now if I cut/paste the whole directory than contains the android studio files into /opt will it automatically get updates when I run sudo apt-get update && sudo apt-get upgrade?
The question also applies to any package installed outside of snap and apt
No. apt-get upgrade only updates packages that were installed through apt.