grammatical doubt over unfinished timeline contexts

Grammatically, we go with present perfect when referring to the actions where the time is still unfinished.

I have phoned him today.
I have watched a movie this week.

But to have a conversation over what happened today, should it be completely in present perfect as the time is still unfinished or past simple?

For example, do we always use auxiliary verbs to create the present perfect:

1. I have called him today, he has answered the call and has given the details of the project. We have also discussed several other things regarding the project and he has given a detailed explanation.

Or can they be omitted, using the past simple?

2. I called him today, he answered the call and gave the details of the project. We also discussed several other things regarding the project and he gave a detailed explanation.

In some cases, it does appear to make a difference:

3. a. Peter watched this movie many times this week (If we just use past simple in this context, does it mean that peter is dead?)

   b. Peter has watched this movie many times this week.