What happens with your apps if you restore from iTunes backup? It is my understanding that restoring from iCloud causes apps to re-download automatically. If, however, I backup to iTunes, and iTunes does not have copies of my apps in the library, and I need to restore the device, what happens to the apps? My guess of what the desired operation should be is that the iTunes backup tells the device which apps it should have, and the device could then start automatically downloading them from the app store, organized the way they used to be and all (with the hopes being you have enough bandwidth for 5GB of app downloads). Is that how it works?

And is there any way to backup apps from the device to iTunes to avoid the bandwidth issue?
Indeed: restoring from an iCloud backup works the same way as restoring from an iTunes backup and all of your apps will automatically redownload.