In general, on common Linux file systems, the operations are afaik not audited.
So all you can say, that someone with write permissions to both source and the target directory moved the folder.
Additionally, you seem to believe that you are connecting "to WinSCP". You are not. WinSCP is just a client. Most of your issue is about the server you are connecting to "with WinSCP". You need to talk to your server administrator.

My folder /axp/buanalytics/csfdsgmns/dev/hmansell was moved into another folder by accident within the csfdsgmns/dev directory. Now it is in /axp/buanalytics/csfdsgmns/dev/fliu6. I don't know if I moved it, or someone else with access to the shared directory. The move happened at about 11am this morning. I need help with the following:

• Is there a way to know what person's credentials moved this folder?
  
• All of my database tables within the databases of my folder are now empty. Is WinSCP backed up somewhere, so that I can pull from the databases tables before they were emptied?