Since you are a EU citizen, i think you don't have any problem with interrail.

Hi yes usually  the country of Residence counts but as you may have a ItalianPassport? it´s no problem to use Interrail with your Italian Passport (just note that you are then limited in Italy  and can  use your Interrail only for 2days there.) 

(did I understand it right, you have buy an Interrail and selected UK as home country?)

You need a document that says that you are living in UK during your trip , when it can happen than some train conductor asks about that (but very uncommon) , than you are ok.

Wich citizenship you have is not the point, but when they check documents, they look if your citizenship is the same of the home country. 

I am residing with family in the UK.. I an Australian but I will be living there for 3 months. What kind of document do you suggest I could get to prove that? Or will it be insufficient. Honestly, I just want an exchange to the Eurrail pass but this deal says non exchangeable. 

Then-AFAIK-you are under the normal rules as being tourist (MAX stay either 3 or 6 monthes allowed) and you will not get any official docum that you are registered In UK. This nearly always implies you have to have some type of VISA to stay legally in UK for longer periods and that would serve as proof of. Unless it has to do with Britsih commonwealth & all that-you cannot expect normal EU citizens to know all about that what they will never encounter.

This grey area of who lives where-esp. when its outside own country gets more complicated and murkier by the day with all the exceptions etc.