How to recover Mail, Calendar and Contact after Mavericks to Mountain Lion downgrade? I want to downgrade from Mavericks to ML. If I do this, how can I recover my emails, calendar and contacts after the downgrade?
Mail isn't stored on your Mac but on a server of your provider and will backup automatically after sining in again in Mail-App on ML   

Export all your contacts by selecting all -> file -> export -> vCard
import the vCard on ML in Contacts file -> import  

For Calender, you can select single colored event-collections and export them
file -> export-> export  

After that copy all files you now made to an USB/external drive and use them again on ML

Usually all these things should also be stored in the cloud, so they won't be lost when downgrading, best check this before downgrading on iCloud.com