"The storm is coming."
I don't think we've seen that verb before, is it a synonym for באה or is it a storm specific word?
I moved on from the exercise so now I'm not sure but I think it was מגיעה. It was in a tap the words exercise, and the only word that I didn't know.
What is the difference between a storm and a tempest?
You can treat these two words as synonyms. There may be some subtle cases where one is appropriate but the other may sound irregular, but generally, when you learn a foreign language you usually don't get such subtle differences.
If you're talking about a real storm - like when there are strong wind and heavy rain - you can use either. If your storm is metaphorical, like strong emotions within your mind, then סערה is appropriate, but סופה is not. If you're brainstorming you'll use a verb derived from סערה, we call it "סיעור מוחות", not anything derived from סופה.
So as a summary, use סופה only for weather, and only when the winds are strong. Otherwise, use סערה. In fact, you can always just use סערה.