How a DBA can monitor multiple huge SQL Server databases more than 2 tera bytes
Lots of questions so many answers. It depends on so many factors. Budget being one.

First of all I would like to point out that visiting some basic SQL Server courses will vastly increase your understanding of SQL Server and its requirements. IMHO switching from Windows Server Administrator to SQL Server DBA is not just something that can be accomplished by querying Google or asking questions in a forum. You can acquire some knowledge, but without the full picture, you are liable to break something in a productive environment.


Do a search for SQL Server Monitoring Tools in Google. You should get a list of well known products back.
That depends on the monitoring software you purchase. Some can handle these requirements some not. There are also freeware tools available that could help with certain aspects.
Some monitoring products can handle up to 200-250 servers per instance depending on the load and the frequency of polling.
Brent Ozar has an article on this aspect: How many servers can one person manage?, and then again: it depends.
So many aspects here:


Don't hand out the sa password! Never!
Windows Server admins are not DBAs and should not have access to the SQL Server instance. (My opinion)
People outside of the Server or DBA team should not have access to backup drives or to SQL Server database file locations.
Only a qualified DBA should be allowed to be have sysadmin server role
Limit each SQL Login/NT Login to the least possible number of databases.
Limit the SQL Login to different roles depending on usage


DB_NAME_User : db_datareader, db_datawriter
DB_NAME_Dbo : db_owner

Try Transparent Database Encryption
Try Database Backup Encryption



Security depends on the requirements of your business. Ask the head of IT for SLAs or OLAs and any company-wide security policies, etc.

One question you haven't yet asked is: Availability. Will you be required to have Always on Availability Groups?

You asked a lot of questions, I hope you have a general starting point.