Did you really get
three of each "Iron Eagles Down!", "Missing Child" and "It's The Zombies!"?
Edit4: And, no, the events are not supposed to pop as often as that.
Edit: Otherwise, the problem is not doing better in missions. That is indeed not possible. But each Cult Apprehension you miss (as in, do not reach) is 200 score down the drain, and you seem to have done 9/14. That by itself is about -1000 right there.
Edit2: Two missed Madman Rampages are another -600, and the crop circles and cattle abductions are another -400. And for comparison, your total mission score is 58.
Edit3: Still not sure why you have such a negative research score. That single flaslight research is not enough for that.
Also, you seem to not have read most of the Ufopedia. Some of the problem might be there as well, if not now then in the future.
Edit5: I tried a beginner game for comparison, and the first month (with 'month 0' missions and all) gave me -3k score when I did nothing (and virtually none of that came from events). So, yes, the big lesson here is
to do every mission. Because the Council is watching.
Edit6: Counterintuitively, Beginner difficulty actually makes the game harder to a degree, since there are less enemies and thus less loot and score on every individual mission.