Many EU airports are the same. It is indeed 脑残

If I have internet access already, WHY would I still need a free wifi?!  really dumb set up.

As your train issue, both Trenitalia and italo have a BOOTH just in front of the platform entrance - you just need to go there to get this thing fixed.  Very easy.

Besides, why use Trenitalia versus the private train italo now it has many routes, with all major routes covered.  Much nicer seats if you take Coach.  If you take first classs then Trenitalia actually slightly better for those travel as a group because they have 1 and 1 sits face to face with a small table in the middle.  Very handy for 2 persons travel together.

F is not much more than coach, may be 30% higher when buy it early.  WELL WORTH the extra euro spent.