If I borrow one license from my ArcGIS concurrent license server will the server count get reduced? Altogether the institute is having 5 licenses; if I borrow 1 will the available ArcGIS license count be reduced to 4?
Yes, borrowing a license means it will be unavailable for use by anybody else until you check it back in. You don't suddenly gain an extra license.
The timeout for borrowed licenses is defined by your license administrator. Contact your organization's license administrator to change this value. The default timeout is 30 days. If licenses are not returned within that time, they will automatically be disabled on your machine and reenabled on the license manager.