Physical Chemistry - Rates, Half-Life etc

To identify the half-life look at the initial value (at 0) and when the value halves (at 480s). For the order, identify another half life. If it's still the same time (which it is) then the reaction is first order. To calculate the rate constant you need an initial rate.
Alternatively if you have a Facer book for A2 look at page 11 at the bottom. For this reaction, rate=-d[ester]/dt is an approximation that measures the average rate during the period. For first order reaction rate=-d[ester]/dt=k[ester].
From that you get kt= ln[ester0] - ln[esterT]. Ester0 is initial, esterT is conc at time T. After one half life [ester1/2]=1/2[ester0].
From that you can rearrange and get k=ln2/halflife(in seconds). As you can see it's very complicated so I'm guessing somewhere there's a rate.

For part b the stochiometry indicates the reaction is first order as the half-life is constant. I have no idea of the order you found from the experiment.