T-SQL code to get the active Connections for each Database.

--Method 1

 SELECT 

    DB_NAME(dbid) as DBName, 

    COUNT(dbid) as NoOfConnections,

    loginame as LoginName

FROM

    sys.sysprocesses

WHERE 

    dbid > 0

GROUP BY 

    dbid, loginame

--Method 2

EXEC sp_who2

--Method 3

SELECT  spid,

        sp.[status],

        loginame [Login],

        hostname, 

        blocked BlkBy,

        sd.name DBName, 

        cmd Command,

        cpu CPUTime,

        physical_io DiskIO,

        last_batch LastBatch,

        [program_name] ProgramName   

FROM master.dbo.sysprocesses sp 

JOIN master.dbo.sysdatabases sd ON sp.dbid = sd.dbid

ORDER BY DBName,spid

Script to find Windows authentication mode/ Mixed authentication mode in SQL Server using TSQL

DECLARE @AuthenticationMode INT

EXEC master.dbo.xp_instance_regread N'HKEY_LOCAL_MACHINE'
 ,N'Software\Microsoft\MSSQLServer\MSSQLServer'
 ,N'LoginMode'
 ,@AuthenticationMode OUTPUT

SELECT CASE @AuthenticationMode
  WHEN 1
   THEN 'Windows Authentication'
  WHEN 2
   THEN 'Windows and SQL Server Authentication'
  ELSE 'Unknown'
  END AS [Authentication Mode]