Why do protic solvents speed up the rate of Sn1 rxns?

Question

Also why is I(-) a better nucleophile than F(-) in protic solvents?

Answer 1

The SN1 reaction between a molecule and a nucleophile takes place in more than 1 step.
The first step is the rate determining step: Formation of a carbocation from the molecule by separation of a leaving group from the carbon; this step is slow and reversible.
The second step is nucleophilic attack.
Since the SN1 reaction involves formation of an unstable carbocation intermediate in the rate-determining step, anything that can facilitate this will speed up the reaction. The normal solvents of choice are both polar and protic. Polar to stabilise ionic intermediates in general, and protic to solvate the leaving group in particular.
For your second question, I believe that F- is much polar than I-, thus F- may easily leave to form a carbocation.