Why should I care about atmospheric extinction?
The answer is a bit long, and treated on the welcome page
How low can the stars be before worrying about extinction?
As long as the comparison stars and the variable star (or object of interest) have the same altitude, you don't have to worry about extinction. However, the lower they are placed, the more the differences in altitude start to matter. As a rule of thumb, if you go below 20 degrees altitudes, consider correcting for extinction if your variable and comparison stars are placed at different altitudes (more than one degree difference).