There should be no requirement for username or password in live session.
If you are trying to install apps in the live session, you cannot. Live USB is read-only unless you created a writeable partition during USB installer creation.
Based on the boot video it looks like the downloaded iso was corrupt as it mentions that there was an error with one of the file checksums.
We would recommend you to try downloading the Zorin OS .iso file again using the latest version of Firefox or Google Chrome without any third-party download managers (in order to avoid file corruption). You can verify whether the file has been downloaded correctly without corruption by verifying that its sha256 checksum matches the one listed after pressing the "View sha256 checksums" button here.
To verify the checksum, we would recommend you to use an app called QuickHash, which can be downloaded from here: https://quickhash-gui.org/downloads/
After opening QuickHash, please navigate to the "Files" tab and select the "sha256" Hashing Algorithm before clicking the "Select File" button to choose the Zorin OS .iso file and waiting for the checksum to be generated.
If you have verified the sha256sum for the iso (and it is correct) then it appears that there may have been an issue with your installation medium, as USB drives may experience wear & tear from extended use. If possible, we would recommend you to try burning the downloaded Zorin OS .iso file to a different USB drive.