That's happening because you have the Help>CheckForUpdates>AutoCheckAtStartup option enabled.
Google domain is pinged to find out if computer is connected to the internet and the statcounter is a web statistcs service I use to understand the panorama of PDF Explorer trial users. No private information, other than a normal web browser send to these statistics services, is collected, so definitively not spyware. If computer is indeed connect to the Internet, the check for updates feature will then get the updates information from PDFE site and present it to user, if any available.
Just uncheck that option, and manually check from updates, if you don't want to contribute to my statistics data
