The primary alcohol is sterically more available than the tertiary alcohol. Note that a radical path requires breaking a very strong O-H bond, and is thus not a reasonable mechanism. The base deprotonates the activated position. A second deprotonation is possible, but I will accept your answer if you wait until after the C-C bond formation. Acid catalyzes dehydration.
Nucleophilic addition is one rate-limiting process.
The tertiary reactant in a polar solvent should lead to an S N 1 pathway. B. Racemization is the normal outcome for an S N 1 reaction. Recall that carboxylic acids exist primarily as H-bonded dimers and are less polar than the unimolecular structure suggests. Clearly formation of a tight ion pair must be a key component of the mechanism, and that dissociation to at least a solvent-separated ion pair must be part of the mechanism where racemization is seen. Trifluroethanol is an oddball.