Kate,
re your question about pushing the carts by yourself at eze. Yes, you can handle it all by yourself, although I have seen porters hanging around baggage claim if you need one. It's a pretty short push from baggage claim where you get the free carts, to the x-ray m/c. It's also a very short push from the x-ray machine out into the very first lobby where there are 3 or 4 taxi booking company kiosks. If you stop here and book (and prepay for) a taxi at one of these kiosks (VIP Car, for example) they will help you push your carts all the way to the taxi parking area. It's all on one level, there are no stairs elevators or ramps.
Good luck.