Can an android app cause my phone to reboot?
An app can certainly deliberately reboot the phone, depending on the permissions for the app in question and whether it has root privileges.

An app can also force you phone to reboot if it bombs out and takes Android down with it, particularly apps that interact with phone functionality (volume adjustors, automatic task killers - which are a bad idea in general, location aware apps, etc)  If an app has the right permissions this can happen quite easily.

So to sum up, yes, it's quite possible that an app could be causing the system to die and your phone to reboot.  If you want to troubleshoot, you can use Titanium Backup to freeze one app at a time to see if that alleviates the issue, or you can just uninstall and then reinstall later on.