The first form is incorrect, because the verb should be past tense:
"Today, she talked to me by phone from the middle of Italy. What ..."
The reason is that this appears to be relating to 'reported speech', that is, someone repeating something someone else said to another person some time later. The introductory sentence is therefore talking about an event in the past, and so the tense should match that. Regarding the tense of the rest of the paragraph, if this analysis is correct, it should probably be:
"Today, she talked to me by phone from the middle of Italy. What was she doing there? She was working on her novel."
The second version I think is also incorrect, though for a different reason. If this is in fact present tense -- that is, in the context of the paragraph the action is happening in the present -- then the word Today is not needed. Being present tense, it is necessarily 'Today'.
She is talking to me by phone from the middle of Italy. What is she doing there? She is working on her novel.
Without that first word, it almost works though the second sentence doesn't quite work now. There is one last point though. If in the here-and-now "she is talking to me" then it cannot be the case that "she is working on her novel". The same issue does not arise in the past-tense version because you are not specific about when in the past things happened.
So, an attempt to fix it might result in:
She is talking to me by phone from the middle of Italy where I interrupted her work on her latest novel.
Overall, writing things like this in the present tense is hard, though can be justified when you are telling a story and want to keep the reader feeling engaged.