I'll start by correcting a few things in your question: If somebody CALLS me and says: Hi, Can talk with Rosi?* WHAT is the answer? *'Can talk with Rosi?' is not wrong, but the usual question, especially in a more formal situation is 'Can speak to Rosi?'. In a less formal situation, we would usually say 'Can talk to Rosi? As for the answer, option 1 is fine. Option 2 isn't quite right. We would usually say 'That's me'. A third option, only used on the telephone, is simply 'Speaking'. This is an example of 'telephonese', and is the short form of 'This is Rosi speaking.'

Both options are ok. You can also answer: "This is she" (I believe this may be grammatically incorrect but it's very common to answer this way) or "Speaking"

Either of those is ok.Or you can say "Yes I am Rosa, or even just "Rosa speaking" if you are on the telephone.