* I have a headache ( ) and a stomachache. ( )

Listen carefully, and if the expression has a rising intonation, mark an upward arrow. If it has a falling intonation, mark a downward arrow in the parentheses.

In the sentence, before 'and' it has a rising intonation, so you should mark an upward arrow in the first parentheses. However after 'and' it has a rising-falling intonation. So you should mark a downwardarrow in the second parentheses. It has a falling intonation at the end.

(Is my explanation correct? Do I have to use 'a falling intonation' or just'falling intonation' without 'a'?)

You have phrased this well. Smoother phrasing is if you write this without the "a" before "rising..." or "falling..."