I go to say that thanks to the prompt and impeccable technical help from EA, after almost a week I successfully recovered my account thus saving 2 years of progress and I am now back in.
For all of you out there having the very same problem here is the solution which saved me, step by step:
1 - do an immediate encrypted backup of your iphone (5SE in my case), this works better than any syncing to EA/Facebook. All your progress is now safe on your Mac/PC bulletproof ready to be reinstalled.
2 - email EA for support and get no reply.
3 - post on this forum and discover many other users having the same problem. Still, no one from EA posting anyone a reply.
4 - search (a lot) for a customer assistance number for Europe, call them and listen carefully to their explanations. You will learn very useful new things like how to turn off your mobile phone, restarting it and even how to close apps in background or check if your iphone is connected to the internet.
5 - go and buy an iphone 7 or better
6 - put your old iphone in airplane mode
7 - install your backup from step 1 on your new shiny iphone 7 (or better)
8 - enjoy PvZHeroes (in my opinion the best card game on mobile devices, sorry Hearthstone)
I hope this will help!
Ciao
