If you want index to be included as a field in the incident itself, you could add "index" as an incident review event attribute.
Configure > Incident Management > Incident Review Settings > Incident Review - Event Attributes
For this to work you would also have to make sure that the index field is included in the output of your correlation searches as well. This would require edits to a lot of the out-of-the-box correlation searches that use the tstats command on data models.
It depends. Often alerts are fired based on the output correlation searches and these are usually baked by data models.
The easiest way would be to check if your incident review event has shows something like the original sourcetype. From there you should find the source index relatively quickly.
Another option would be to check the actual SPL in the given correlation search in each incident review event. You'll see, which datamodel/s is/are used to get the data from. From here, you could either look for the specific datamodels in your
Enterprise Security -> Configuration -> CIM Setup
Global Settings -> Advanced Search -> Search Macros -> cim_[Datamodel]_indexes