You should check with your seller but it seems to me that it is no longer possible to download versions lower than 2017.
Also pay attention to the compatibility of the windows version with the 2016 (https://files.solidworks.com/Supportfiles/Release_Notes/2016/French/relnotes.htm)
To your question [Do I need to uninstall SW2019 and 2021 to be able to install 2016?] The answer is no, don't uninstall them. On the other hand, follow the installation advice of our colleague@stefbenoso that the different versions don't step on each other's toes.