The mechanisms for these reactions aren't required by any UK A level syllabuses, but you might need to know a little about the nature of Grignard reagents.
A Grignard reagent has a formula RMgX where X is a halogen, and R is an alkyl or aryl (based on a benzene ring) group. For the purposes of this page, we shall take R to be an alkyl group.
The Grignard reagent: Preparation, structure, and some reactions
Grignard reagents are made by adding the halogenoalkane to small bits of magnesium in a flask containing ethoxyethane (commonly called diethyl ether or just "ether"). The flask is fitted with a reflux condenser, and the mixture is warmed over a water bath for 20 - 30 minutes.