Step 1: Recall SN1 basics.
SN1 goes in two steps through a carbocation. Its rate depends only on the substrate, so the nucleophile strength does not matter, and polar protic solvents help. Those three statements are true.
Step 2: Test the nucleophile claim.
A strong nucleophile would rather attack the substrate directly and push out the leaving group, which is the SN2 route. So a strong nucleophile favours SN2, not SN1.
Step 3: Pick the false one.
Saying a stronger nucleophile favours SN1 is wrong.
\[ \boxed{\text{Stronger nucleophile favours SN1, option 1}} \]