Simple present, or present continuous?

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.

Present simple is used regular actions or habits, or for facts that are always true.

The word today is key, and it's used with the present continuous, because it's not a permanent situation, it's a temporary situation.

Present simple is often used with time expressions like usually, always, everyday, never, on Sundays, etc.

Should the simple present be used or the continuous?

The verb form in the examples is not particularly idiomatic without some context to justify what appears to be the historical present tense.

That said, the simple and continuous forms of all verbs have their respective nuances and you should decide what you want the sentence to mean, and then choose the appropriate form:

All simple forms of the verb indicate an action as a whole - from start to finish.

The simple form of the verb can indicate a habitual or regular action that

(i) is/was/will be complete/completed each time it is undertaken.

A: What do you do to keep fit?

B: I ride a bike. -> “ride” includes everything from getting on the bike at the start of the journey to getting off the bike at the end.

Or

(ii) a single, complete or completed present, future, or past action:

"He told me that I had to visit the Eiffel Tower, so I go/went/will go to Paris on Wednesday” -> “go/went/will go” includes everything from the decision being made, bags being packed, going to the airport, etc., to the arrival in Paris.

(iii) a habitual, recurring, regular or frequent action (that is completed each time)

On Saturdays, I go to the gym.

He ate toast for breakfast every day of his life.

The continuous form of the verb indicates

(i) an action that is/was/will be incomplete and in progress at the time that is being referred to (it has started but it has not yet finished) -> I will be/am/was/have been/had been riding a bike = I will be/am/was/have been/had been in the process of riding a bike but have not yet finished riding the bike at the time I am referring to.

The continuous form used to be known as “the imperfect”: It was called “imperfect” because the action had not been “perfected” i.e. it had not finished.

OED 5. Grammar. Applied to a tense which denotes action going on but not completed; usually [edit Q- but not always] to the past tense of incomplete or progressive action.

1871 H. J. Roby Gram. Latin Lang. §549 Three [tenses] denoting incomplete action; the Present, Future, and Imperfect (sometimes called respectively, present imperfect, future imperfect, past imperfect).