Hi,
Thanks for using our Facebook Importer. I can help answer your questions.
We do not have a feature to not show already imported events on the import page.
If you think that is something you would like as a feature I encourage you to visit our User Voice Page and either upvote an existing request or make a new request there.
http://tribe.uservoice.com/
Cron
We already have it setup to import events using a cron with the settings on this page:
Events > Settings > Facebook Tab
However, if you are importing a large amount of events and the server timesout it may not import all the events, which sounds like it might be the case.
Let me know if you have any follow up questions.
Thanks