How to parse the IAT using IDApython?

There’s no built-in functionality for that, it’s too target-specific to be useful as standard API. What you can do is to retrieve the list of exports and/or imports for the file which was used to create the database. If you need the low-level IAT details you’ll have to parse it manually from memory or database (not sure if database keeps enough information so you may need to go back to the input file).