Find name that carries the shift on that day.

Good evening, I ask for your help to find the name of the person you will have to take the other's work while respecting the abbreviations listed in Sheet1 column C depending on the day of the month going from Column E: AT.
The shifts acronyms can be found in the sheet 1 from the A26 line
In October sheet (1) and October (2) I have indicated the due result.
Thanks for your help.

Good morning I tried to do some formula I am attaching the new file.
That's left to do is enter in the formula the two other conditions:
1 - If the day of the week in cell A4 in Ottobre sheet (1) is Saturday the formula with the names in column C have F1.
2 - If the day of the week in cell A4 in Ottobre sheet (1) is Sunday, the formula with the names in column C have F2.
In fact, as you can see in Ottobre sheet (1) is out of the list that Valentina F1, while in Ottobre the sheet (2) remain out Pietro, Valerio who F2.
I hope now it is more clear and that it is possible a solution.
Thanks again.