Does Mac App Store provide an email support channel? I want to know if there's any email support specific for Mac App Store.

Anyone have the idea?
If you purchase an app from the Mac App Store, the purchase receipt you receive via email contains a “Report a Problem” link.  If Apple replies to your problem report via email, that email can contain a return email address for the particular Mac App Store problem you are reporting.

Each app developer is also required to have a support link for that app listed in the App Store.

For general support, Apple recommends using their Support App. See:
https://support.apple.com/contact

There are also Apple community support forums: https://discussions.apple.com/welcome 

and https://discussions.apple.com/community/app_store/using_app_store