Count of open sockets to the database I want to check open socket connection count to the database.

Is there any way to get the number of open sockets to the database?
Yes.  This query will give you the current number of client connections using TCP/IP.  Of course there are other things that use sockets on the server.

select count(*) connections
from sys.dm_exec_connections
where net_transport = 'TCP'


You can see all the sockets usage on the server using the netstat command.