Determining Half-lifes from a graph
At any time, the number of decays per reasonable$^1$ time unit is proportional to the amount of the isotope present. (This is expressed by the first-order rate equation for a one-decay process.) Therefore, it does not matter whether one looks at the amount or the number of decays. It may be easier to measure the number of decays by e.g. a Geiger counter and prefer it for that reason.

It now matters what you understand to be the rate: the number of decays per second or the percentage of nuclei decaying at any given time. The first becomes less over time, the second one is a constant for each isotope.

$^1$ You must have a reasonable number of decays within your time unit. If the half-life is long, it makes little sense to look at millisecond slices.