I too am finding this very frustrating indeed, particularly as I only have three apps, and no music! Two are already on the iPhone, one purchased and one free. The third one is shown on the iPhone panel in iTunes as if it actually were on the phone - with the little box next to it saying "Remove", but is there any sign of it on the iPhone itself? No, there @@@**@@@ isn't.
It's quite true I am new to iPhones: the one I have was gift from someone upgrading to the latest model. But in every other way it seems to work fine.
I get the endless "this iPhone can't be synced" pop-up, telling me to authorise the computer. I do that and the ITunes Store tells me the computer is already authorised. Over and over again. About the only thing to be said for it is that I am unlikely ever to forget the password I'm using, I've typed it so often.
The phone and the account were originally in the UK and they are now in France, but the iTunes account is now properly set for France (it allowed me to buy and install the only paid-for app a week or so ago).
I'm trying to get the free version of Strava onto the iPhone and Mr Apple just won't let me. Perhaps he doesn't like cyclists?
Suggestions would be very welcome. I have already tried virtually all the ones in this thread, except doing the full re-set on the iPhone and re-installing everything. I don't want to lose the couple of apps that are actually there.