You've reached the right place for help, NWMan.
Let me breakdown your questions a bit to make sure everything is addressed.
To answer your first question, yes, QuickBooks Desktop 2016 has the same multi-user feature as the 2011 version. However, I'd like to inform you that QBDT 2016 has already been discontinued. Thus, I suggest upgrading it to the latest version so you can continue working with the offered online services.
Learn more about the discontinuation policy by checking out this article: QuickBooks Desktop service discontinuation policy and upgrade information.
For your second question about setting up multiuser, you'll want to consider the Peer to peer hosting method. This ways, the computer that has the company file (host) allows other computers to access the file.
Visit this article and scroll down to Peer to peer section to learn more: Hosting your company data in multi-user mode in QuickBooks Desktop
Regarding your question about arrangement work between different versions of QBDT (2016&2020), this is not possible. Once company file is being updated to a higher version (2020), you can no longer open it in the older version (2016). Having multiple users in different computers is only applicable within the same versions.
To learn more about multi users in QuickBooks Desktop, please check out these articles:
I’ve also included this troubleshooting guide in case you’re having issues when you try to switch to multi-user mode. I’m sure this will be helpful.
For your last question, QuickBooks Self-Employed (QBSE) is considered to be a different platform. Thus, you'll need to subscribe to a separate QBSE version.
I'll leave this link that provides comparison among different QuickBooks versions: https://quickbooks.intuit.com/products/
You know where to find me if you have follow-up questions while setting up multi-user in QBDT. I'll be here to answer them. Have a great day ahead.
