how to use 'periodic import'

yes, it is very useful. For example you may have a site where a View is used to create/maintain a CSV or XML feed. Then another site will consume it on schedule. So when one site has new content, it is updated on the other site after the periodic update.

Yes - Documentation on Periodic import will be very much needed.

It seems that, Periodic import never gets executed if we run the Cron.

In Feeds 7.x-2.0-beta4 you will no see the next import time on the import page. If content doesn't seem to get periodically updated, you can now see on the import page if it is actually scheduled.

There are some cases where importing during cron does not work even if it is properly scheduled. See #1995728: [META] Cron import not working on 7.x-2.0-alpha8 and later for the general issue about this topic.

Mine works well on 7.x-2.0-alpha9 although it may miss importing on occasion but I don't know for sure. In either case it seems to be working for a number of years because there are no complaints from the various organizations where this is utilized. I check every once in a while to see if it is working and it is.

We utilize both CSV and XML feeds produced by Views from Source sites and those are consumed by Feeds attached to Content Types on other sites. The feed must stay attached to the content type, and once attached, the imported nodes cannot be directly edited. You can un-attach it but then it will no longer auto import.

The first node for that content type should be the CSV Importer at where you will provide the url to the feed.