Q - Some correlation searches didn't use Data Models and just used simple search commands, how I can change these correlation rules to use our indexes?
A - please find out the correlation search and then you can edit/update it.
this is the list of correlation searches available from ES.
Q - at first, is it needed to change anything?
A - depends... many times advanced splunk admins want to edit the correlation searches, so they find out and edit them. but, also, most of the cases, default things works perfectly as well. so it all depends on your requirements.
Q - My second question is which permission or user will ES use to run Correlation Searches? I mean I have to grant access to our indexes to which Roles/Users?
A - i am not sure, but as per my understanding (of base Splunk product), to edit/update a correlation search, there will be no needed of role/access/ issues.
but, it seems Splunk ES provides a role "ess_analyst" which can be used to manage correlation searches.
you can try to find the correction search and try to see if you got edit option. if you dont have, then, probably you will need this role.
(i have got the 100 karma givers badge, how many karma points you have given!?!?)