Can it be "when taking the shot" instead here?

What's the main difference between a "teacher" and an "educator?"

An educator is any person whose job it is to educate others. So in addition to teachers, who are educators, this can also include professors, tutors, and instructors. This term is quite broad. Every teacher is an educator, but not all educators are teachers, as teachers are specialized in teaching and often require some sort of teaching license or certificate to teach. Teacher = educator BUT not every educator = teacher.

Why is "doing" necessary in this sentence? Can't I just say "drawing"?

Great question. Actually here the word "drawings" is the plural noun meaning pictures. It is not acting in its verb form. Because of that you need a verb before it to show the action, in this case, "doing". Taking doing out of the sentence would make it grammatically incorrect. You would have to change the sentence to "the children were drawing" in order to maintain grammatical correctioness. Ex: I'm drawing a picture for school. = I'm doing a drawing for school.

When do you use "gang" to refer to a group of people?

The word "gang" can be used colloquially to refer to a group of one's friends. Its original meaning usually carries an implication of illegal or otherwise immoral activity, but it is used almost ironically to refer to one's friends in this context. The original, literal meaning can be understood as "organized group of criminals". Ex: Hey gang, let's work really hard today and finish all our tasks! (colloquial) Ex: A gang of teenagers has vandalized the local bank. (original, literal meaning)

Why would he mention the word "sleep" in this context? Is it a metaphor?

So, I think there are two meanings to this. First, there is a common belief that people love to "waste" time on technology, like using cell phones until late at night which prevents us from sleeping. Tim Cook is maybe referring to that when he says that "it's technology that helps you sleep, not keeps you up" to state that the function of the technology is going to be the opposite of what it is doing right now. Secondly, "to be kept up" is often a way to state that one's worries make it difficult to sleep at night. Indeed, privacy concerns can cause people to worry. Thus, Tim Cook's statement might mean one or both of these meanings. Instead of stimulating us to stay up late at night (either due to time-wasting technology or privacy worries), the technology is intended to make us feel secure and safe.

What does "tenant" mean?

A "tenant" is a person who temporarily rents and lives in a house or apartment owned by a landlord. Ex: The landlord has twenty tenants. Ex: I am a tenant at this apartment complex.