Request always going to default

"Path shows correct. But is not matched in irule even though query is exactly for that same path, so no logs are seen for the path."

Then the switch statement must be incorrect - do you have the right case?

"Is there a way to have two separate cookies one set in the irule and one for default. "

Yes. Set a cookie based on cookie insert (give the cookie a relevant short name - I hate seeing cumbersome BigIPxxxxxxxxx cookies) and assing profile to virtual. Then your iRule will not complain when you say "persist cookie insert jj_cookie". Beware of this though; http://support.f5.com/kb/en-us/solutions/public/11000/600/sol11679.html you can get round it by creating a profile for a session cookie with the cookie name jj_cookie.