How can I sync my iPad apps onto a new iPhone?
No, you're not. The iOS device is a consumption device - every time you toggle the app sync option it will try to "reset"/wipe the existing apps and re-transfer them. Either leave that option on or tweak it and set your sync to Manual. 

To sync your apps to a new device, you have to transfer as to it as a new device. Existing folder structures you had on the iPad do not transfer to phones. You cannot restore configs between different devices.

New phone = new setup of apps and their folders. You sync between your iTunes library and device not device to device.