SN1 vs. SN2 is a little less clear cut, but in this case it is almost certainly SN2.
The difference is whether the Cl leaves first and then the alkoxide adds or whether the alkoxide forces the Cl out while attacking the carbon all in one motion.
The "substitution" refers to the carbon with the leaving group attached to it. In this case the net change at that carbon is that the chloride is substituted for an oxygen in the product. In an elimination reaction, however, the chloride would just be gone with nothing taking its place (the carbon would only be attached to three other atoms).
The DMF doesn't directly play a role in the reaction mechanism and it remains unchanged.