Iodide is a very good nucleophile, and chloride is a good leaving group, and the carbon is primary - so even in a protic solvent I'd still predict SN2.
As Azmanam said, when considering how good a leaving group is, think about it's stability. The chloride ion is quite stable - consider how easily HCl dissociates - and so is a good LG. Note that this is also why iodide is a good leaving group as well - it is a good Nu and a good LG. As a result iodide can displace itsself in an SN2 reaction - if an alkyl iodide has an asymmetric centre at the carbon bearing the iodine substituent, treatment with iodide can induce racemisation.
You are correct about 1-chloropentane reacting faster than 1-chloro-2-methylbutane. Bulky substituents adjacent to the (as well as at the) reactive centre will hinder the nucleophile - the classic example would be neopentyl compounds, which have a tertiary position adjacent to the reactive centre - e.g. 1-chloro-2,2-dimethylpropane - these react very slowly by SN2 due to steric hinderance, and only very slowly by SN1 because the carbocation intermediate (which usually rearranges in this situation) would still be primary.
Yeah, Finkelstein is a great name! Maybe only beaten by the Chichibabin reaction.