In general I would treat it matter-of-factly.
Here are some ideas.
(1) Cognitive approach. It can be reassuring to look up some statistics together and post them on the refrigerator where they can be referred to as often as needed.
I have a child who is prone to anxiety, who had intrusive thoughts at about age 6 or so when his other parent was traveling by plane for work. He was afraid Parent would die in an airplane crash.
We looked up the statistics for death by flying, and compared the number of deaths per year to the number of flights taken per year. That fraction is what we put on the refrigerator. The tininess of the fraction, and the hugeness of the denominator, were quite reassuring for my son. Yes, there was a non-zero chance of a plane crash, but the number was so small he felt reassured.
(2) Humor. When that same child developed a fear that an airplane might drop bombs on our town, my partner developed an elaborate fantasy of our next-door neighbor Mark having a secret arsenal in his basement, that he would use to defend our town. It was entertaining the way my spouse did it. The houses in our neighborhood don't have basements -- they're all built on slabs. Also, neighbor Mark was such an innocuous guy -- leaving for his teaching job at a local college every morning at the same time, in his neat suit and blue tie, and always putting on a straw hat to mow the lawn on Saturday, and always going out to the driveway for after-dinner ice cream cones with his daughters. So the details sounded patently ridiculous. The story started like this: Well, we don't need to worry, we can rest easy, because Mark is on the job! And then came the long, detailed description of Mark's tremendous anti-aircraft arsenal in his basement. It was obvious to my son that it was a game. Since the story got repeated every evening, it became a fun ritual that he looked forward to.
(3) Critical thinking. Gradually help your children look at rules with a critical eye, distinguishing between rules that make sense, and rules that don't. It could be helpful for a child to appreciate that the rules that don't make sense are there to reassure some bureaucrat or politician. You can draw some analogies -- e.g. an ostrich with his head in the sand. Here's another analogy: I had a very stupid cat who liked to poop in the bathtub and then try to hide because he thought he was going to get in trouble. He would try to hide under the sofa, but he was too big to get more than his head under the sofa. But he was so stupid he thought he had succeeded in hiding! He thought that if he couldn't see us, we couldn't see him. You can also develop the idea that people can sometimes find reassurance in some rather strange things!
(4) Safe place. Develop the concept of a safe place, and going there in one's imagination. That way a child can get better at self-soothing when parents aren't there.
(5) Modeling. The younger the child, the more you'll want to simplify, but the basic idea is to let your child see that you feel fearful or anxious (about something else), and then see you dealing with it constructively (for example with three very slow deep breaths -- counting with fingers while watching a second hand, maybe hissing on the outbreath). This shows that it's okay to feel fearful or anxious (validation), and it demonstrates a practical way of coping with the feeling.
The older the child, the more honest you can be about your own feelings and opinions, and the more you can work on critical thinking.
Your specific questions:
- How can I explain the situation to my children without scaring or
scarring them? See above. Explain that some politicians and bureaucrats don't have anything better to do with their time than invent silly drills for children to do at school. But we don't want their teacher to get in trouble, so let's humor them and do the drills.
- What questions can I ask them to uncover hidden or unresolved fears and anxieties? *I think that in most cases, as long as you have conversations about feelings, and acknowledge and validate their feelings in general, you'll probably be able to detect how they're doing with handling their fears and anxieties. However, if you suspect the fears and anxieties are starting to be too much for a particular child to handle, then therapy might be something to consider. There's a questionnaire at the back of John S. March: OCD in Children and Adolescents : A Cognitive-Behavioral Treatment Manual that can be used to evaluate for intrusive thoughts.
- When, or at what age, should these things be discussed, alternately how should they be approached at each stage of life? Like everything else, it's a continuum. Start out simple, and gradually go in more in-depth. In kindergarten there's generally a unit on feelings, where they practice recognizing and labeling specific feelings.
- What mental and emotional tools can I teach them so they can deal with these worries and anxieties in unfamiliar situations? See my list (1-5) above for some ideas.
- Where do I find additional resources to help me - in terms of keywords or search terms - for either books, instruction, teaching,
or professionals to help me tackle this issue? Here's an article that might be a starting point: http://kidshealth.org/en/parents/anxiety.html#.
Two more ideas. One is that one can make fear a more tolerable thing to experience through very gentle desensitization. It's kind of like taking a miniscule dose of cyanide every day, to inure yourself to the poison. The key with the cyanide and the fears is not to overwhelm the child. If you're interested in this, you could look into Exposure Response Prevention exercises.
The other is that it can be helpful to partner with your child's school in the elementary ages. Ask how they will be handling these topics, what language they will use, what they're planning to avoid in each of your young children's grade levels. If you feel a teacher is planning something that would overwhelm your child, speak up. You might want to keep your child home on the day a video too disturbing for your child is going to be shown.
(I learned this the hard way, after my son's fourth grade teacher showed a video on 9/11/2012 that showed footage of Sep 11th attack victims jumping to their death. The following year I anticipated the problem and asked the teacher a couple of days in advance what her plans were for commemorating 9/11. Similarly for Martin Luther King Day.)
My sources: taking my son to evaluations and treatment sessions; reading about anxiety and OCD. (The son who's prone to anxiety has an OCD diagnosis.)