Can I get a notification when any of my sites get in or out of the first page of results in the search engine?

Yes. "First page" on most search engines (Google for example) means the first 10 results.

• At the left menu, under Reports, click Reports Center -> Notifications -> Trigger Notifications. 

• At the top-right click the Add New Report button.

• On "Send a notification when any of the Terms rankings" check the box near Reached Top.

• Type "10" to get notifications if your site gets into the first page.

• Or, at Out of the Top, Type "10" to get a notification if your site gets kicked out of first page.