So can we have something like ? Group 1 can access few fields and group 2 can access all the fields?
Yes, assuming Group 1 is a value of a field that you're conditionally displaying fields off of using CB Conditional. Otherwise CBSubs can protect fields based off subscription.
Also my site requires fighters associated with clubs so is there any way I can link fighters to the club or vice versa?
Subscriber available GroupJive 2.x offers group solutions for users, it can quickly be renamed to Clubs via backend Override parameters. GJ functions similar to how Groups do on Facebook and other social sites.
In the cb list can we have search field whrere they can search range like between 50 to 60?
Only Date fields that are displayed as Age can have a search range, but it's based off date. Otherwise you'd probably need to develop a new fieldtype to offer this or use a multi-select drop down with values 50 to 60.