Is there a way to find out how many patches were deployed for a particular Appli

If it is being deployed from single user account, then you can check for import log for the application which gets generated in 'My Import Logs' folder of 'My Private Knowledge centre' every time anything is imported. You can check when those logs for the particular application were generated to determine how many times it was imported. If you are using multiple accounts for importing the applications then you'll have to check 'My Import Logs' for all of those accounts to determine that.

Actually, that approach is based on User accounts instead of Applications. I wanted to find out a list of patches deployed for each application on say staging environment and when they were last imported.

As per my knowledge there is no direct way of the getting a list of the patches for the application.You can check the news feed from an sys admin account. Every import and export gets posted there. But it won't be helpful if the name of those patches are not following a pattern as Appian does not the store the relationships patches and the application.