Q1 How to measure?
Since rate = change in something divided by the time taken, you can fix the change and measure the time OR fix the time and measure the change, e.g. see what volume of gas is made after 20 seconds OR see how long it takes to collect 20 cm3. This applies to pretty much all the other things you could choose to measure.
You can measure the mass of gas lost (not very big since H2 isn't very dense).
The temperature rise - the faster the reaction, the larger the temp. tise
The time taken for all the Mg to disappear
You could drop the Mg in for ten seconds, then remove it, and titrate to find the new conc. and hence how many mol of acid has reacted.
Q2 controlling for temp.
I wouldn't use Mg + acid, since it is very difficult to control for T in a particularly effective way. Another factor is surface area - when the acid reacts, it makes bubbles of H2 on the surface of the solid, which 'protects' the metal from the acid. It also tends to make it float, so only one side of the metal is exposed to the acid. You then have issues with diffusion of the H+ ions in the vicinity of the metal.
Me, I'm all in favour of clock reactions for investigating rates. Mg and acid, would be one of my last choices.