With an Indian passport, you can choose between Interrail and Eurail. The price is the same but Eurail does not have a limitation on only 2 travel days in Germany for you so that's usually the better option. The EU has nothing to do with Interrail.

Only trains are included in the pass. That means most suburban trains (S-Bahn in Germany for example), but never metro or bus, and trams very seldomly (a few lines in Basel for example that used to be railways in the past). In Italy no other public transport is included.

How are you going to Italy? If that's by train, then you'll need a global pass, since the Italy pass is only valid in Italy.

I am actually planning to take the pass from Milan so basically i will select one country pass. I already have tickets from Germany to Milan. So I am planning to get a 10 day One country pass i.e. Italy. My confusion is majorly which to be bought because i am a student in germany and they say EU resident but somewhere i also read they only include EU passport holder so i will be basically Indian passport holder. 

In that case either would work.

If you have an official German photo ID card then Interrail with details of that card attached, otherwise Eurail with your Indian passport number attached.