Could my data have been accessed on my lost iPhone 4 with iOS 7?
It is only possible if the thief knew (or guessed) your passcode.
If your data was in standard apps(Mail, safari), then there's nothing to worry about, if it was stored in apps that allow for filesharing through the 'apps'-tab on iTunes, then I don't really know how iTunes handles that.
Yes it was connected to the Internet, but it could be with 3G (was it on when it was stolen?) or a public network that automatically connects (like Apple Stores or Starbucks) without needing a password.
Don't really know


In any case, report this to your local police office (bring the serial number, it should be on the box) and let them handle the theft.