How to determine which apps iTunes will copy from iOS, to stop a deleted app being resurrected?
To answer your specific questions:


No, there is no way to find out which apps iTunes would like to sync over before answering the question. Technically I suppose you could look at your iTunes App Library and your iPad's installed apps, but that is not a very realistic option if you have more than a few apps.
As far as I've been able to tell, yes you must delete this app from all devices (iTunes and iOS devices) when you have app syncing enabled. Otherwise it will continue to copy back and forth as devices are plugged in.
Checking the "Do not ask me again" box will have iTunes always perform whichever option you selected the time you selected the checkbox. To reset any such settings, you can go to iTunes > Preferences > Advanced, and click the button that says "Reset all dialog warnings".


In general, given the problem you are having with app syncing, I recommend that you simply disable app syncing. There is no practical benefit for most users in having the apps saved to your computer. Your computer is incapable of playing the apps and generally your iOS device can remove and re-download the app directly from Apple as needed. I disabled my app syncing for the very same reason.