I'll try and make this simple!
Day 1: Working in Lightroom Catalog A. The program starts to lag. Check to see if there are updates. There are, so I update. Once finished and computer is reset, I open Catalog A which is then upgraded to Catalog A-2. I then working in Catalog A-2 for several hours, leave my computer and go to sleep.
Day 2: Open Catalog A-2, get an error message right after opening saying Lightroom is experiencing a problem with the catalog and has to check its integrity, etc. Shuts down, not responding, exit out program, reset computer. Navigate to catalogs folder and only find Catalog A! Missing Catalog A-2, but I still see the preview file for A-2. Try to open Catalog A, it asks to upgrade, I say Yes, it renames to Catalog A-2-3. This new catalog looks like Catalog A and is missing all of my edits from A-2!!!
1. Where did Catalog A-2 go?
2. Is it recoverable?
3. Can I restore Catalog A-2-3 with the preview (.lrdata) for Catalog A-2?
H'm. First of all, if your catalog is upgraded, then you didn't simply install and update, you installed an upgrade. You went to the next major version! So what version of Lightroom were you using and what version are you using now?
I have no idea where your A-2 catalog went, but I doubt it can be recovered. It could be in the trash (recycle bin) however, so check that. And no, you can't restore a catalog from the previews.lrdata, I'm afraid.
What is your operating system?