Here are some answers to your questions.
2. On ISC the site uses it's own Google analytics that doesn't rotate with the members analytics ID. So we are given an option of statcounter. For basic usage statcounter is free but for advanced logs, it is paid.
3. You can't use the google analytics as far as the membership upto diamond level is concerned. You may have to contact the editors and staff to clarify if the platinum members have the features enabled. Google analytics is more powerful than the statcounter as it has more data for you to view and learn from your website.
4. Statcounter doesn't have much features and you can enable it here : http://www.indiastudychannel.com/members/StatCounterSettings.aspx
However if you want to track the performance of your current involvement in ISC then statecounter seems to be the only option.