For #3 the methanol is the solvent, not the nucleophile. The nucleophile is the methoxy ion (-OCH3)which is very strong. If the methoxy ion reacts with the solvent it simply generates another methoxy ion, so the only way for the reaction to go forward is for the methoxy ion to react with the ringed compound. Since the halogen is attached to a secondary carbon and not a tertiary carbon (tertiary is what E1's favor), and the nucleophile is strong, going with an E2 is the best guess.