First, think of the experiment. They are measuring heat change in water. The initial temperature
was 22 degrees but it wasn't plotted on the graph because they started to use the thermometer
after the experiment began. There first data point was therefore around 34 degrees because the reaction already started.
Thermometers take time to heat up, so there is a lag in between the time it is getting an accurate recording and the time of the peak temperature of the reaction. This brings error into the calculations because you do not have the peak temperature. Note that the slope of this graph is negative. This indicates heat is being
lost to the surroundings, which in an ideal situation would not happen because you are measuring the total enthalpy of the reaction in a closed system. So our data is off. How do we solve this?
We extrapolate a line back as indicated in the graph below. This solves both problems. We can assume that the slope is fairly constant, so if we extrapolate back we can get the temperature that is a very close approximation to the maximum temperature increase brought about by this reaction.
As far as your other question goes, if you cut the mass of the reactant in half, you cut the heat released (q) from the reaction by half. It is that simple.