I feel like I should know this, but when we delete a record, we have to specify a reason why, how do we first - modify the drop down that is available, and second, how do we see the reasons, my controller is asking why some invoices got deleted, but I am not able to tell her. Hope this makes sense.

The lists are at Setup>Accounting>Accounting Lists and then go to Transaction Deletion Reasons. I remember the reporting on that is in a super unintuitive place. Can't find it at the moment, so I might have to dig a bit if no one else answers.

For reporting you can check transaction audit report it has reason in it

Don't grant FULL permissions to roles to prevent deletion of records. Require an approved ticket to allow admins only to delete records so that everything is documented and approved. This will save you the hassle of having to remember down the road what happened to the record(s).