I found some more information. It seems that there are some "free" hot-spot in the following public places:
Villa Borghese
Villa Torlonia
Villa Ada
Villa Doria Pamphili
Villa Paganini
Unfortunately I don't exactly know where this villas are and which kind of access you can have. But they are defined public, therefore there should be some possibilities!

Regarding a private phone line, the main operator in Italy is Telecom Italia.
I checked in the website (
http://www.187.alice.it/cgi-bin/di_187/di/187/demand/product/serviceDetailCost.do?channelId=-536887615&tabClicked=Dettaglio+Costi&productOid=10629&BV_UseBVCookie=Yes&pageTypeId=536888874&indexHistory=2) and it seems that you can get the line for less than 12 months, but you have a penalty fee to pay when you want to close the line.
But it's quite expensive:
96 euro for activating the new line
14,57 euro every month (cost of the line)
48 euro to close the line earlier than 12 months
Then you have the cost of the calls....

I also have to tell you that in Telecom no one will be able to speak english... therefore you are better to search for someone that can help you. And, most important... you need really a lot of patience!

Believe me!!!

And for sure you need a codice fiscale. You can ask for it. You find here the form:
http://moduli.deltaservicesrl.it/service/codicefiscalepf.pdfBut I 'm not completely sure about where you can give the form to get the codisce fiscale...

For sure in the so called "comune", thet is the office present in each italian city, where you can ask for all your personal document (identity card, etc..).
You can ask for it also in some italian consulate, but not all...
