1. In the tests with NaI/acetone and AgNO3/ethanol, as described in the experiment, it was found that benzyl chloride (PhCH2Cl) reacts in both tests. Why is this compound able to react under both conditions

See explanation

Explanation:

Let us remember that the Iodide ion is a good nucleophile.  SN2 reaction is  promoted in a polar aprotic solvents like  acetone.

Aprotic solvents like acetone do not favor the formation of a carbocation hence the reaction of Sodium iodide in acetone with PhCH2Cl proceeds by SN2 mechanism. This is possible because the compound possesses a halogen atom(Cl) which is easily replaced by I^- from NaI. The corresponding NaCl formed is insoluble in acetone.

Similarly, when AgNO3/ethanol reacts with PhCH2Cl; ethanol which is a polar protic solvent and a poor nucleophile coordinates with the silver ion in the  PhCH2Cl and enhances carbocation formation (SN1 mechanism operates).

The SN2 mechanism is not followed here because there is no good nucleophile present compared to the situation in the reaction of PhCH2Cl with NaI/acetone.