Linked server issues and administration
Are there any DMVs where linked server info is maintained
  select * from sys.servers gives info about what are the linked servers configured .please see below msdn link for more details  on usage
https://msdn.microsoft.com/en-IN/library/ms178530.aspx

Is there any post/document which gives us more information on how to troubleshoot Linked server issues.
This seems like a generalized question,depending on error message,my basic analysis would start from access issues ,sql error log...If you want to troubleshoot performance issues with linked servers there are many links in SO as well as online to start with.

http://thomaslarock.com/2013/05/top-3-performance-killers-for-linked-server-queries/

Is there a way to find from SQL(2008) Side, how many linked servers are being used and how many are not.. as application team want us to remove the unnecessary linked servers.

This has been already answered here by Mr denny.
https://dba.stackexchange.com/a/5520/31995