Why is the rate of reaction fastest at the beginning?
This is largely to do with how much of the reactants are present.
Let's take this equation
At the start of the reaction, when we first put magnesium in the hydrochloric acid, there is 100% of the magnesium to react with. As a result there will be more successful collisions between the reactant particles. The more successful collisions, the faster the reaction will be.
As the reaction continues, less and less magnesium is available to react: so, thus, the rate decreases until it reaches zero.