What are the real rules for choosing between the simple past and past perfect when both actions are in the past?

It's quite hard to say in any particular case that it's wrong to use the past simple rather than the past perfect. For cases (1) and (2), I would say that the tenses the writers chose are the most likely tenses for native English speakers to use. For (3), we simply don't have enough information to decide one way or the other.

1. The hugs were after the beginning of his confinement, and the verb had heard acquires the entire time frame of his confinement from the since, so the time frame of the verb had heard is before the hugs. Here, the order of events is different from the order they occur in the sentence, so we are likely to use the past perfect.

2. We usually don't use the past perfect if the order of the verbs is clear. Here, the verbs occur in the sentence in the same order that they happen (if this isn't the case, it's a trigger for using the past perfect), and there's also the preposition after in the sentence, so the order of events is perfectly clear, so the past perfect is optional here. You could use it, but most native English speakers wouldn't.

3. There are two events here, and if I ignore the tenses in the sentence, the order of these events isn't at all clear. I would infer from the tenses in the sentence that he either started or resumed his work at the construction site after he was injured in the attack. If he first worked at the construction site, and then was injured in the attack severely enough that he couldn't work, I would consider the writer's verb tenses to be wrong.

(1) When you are unsure about a past perfect tense, try shifting to present perfect, and adjusting the rest of the sentence accordingly. Let's shift "he had heard" to "he has heard." Then we have to shift "They soothed" to the present tense "They are soothing." This is what we get:

They are soothing him with hugs and the first kind words he has heard since the beginning of his chastisement.

This seems right, because the kind words he's hearing now are the first kind words he has heard since etc.

The second version you proposed doesn't mean quite the same thing. Note that "since" is a special word and generally gets used with present perfect or past perfect because it's used for some sort of ongoing action.

Note, you could say

Those were the first kind words he heard after beginning his chastisement.

But as soon as you switch to "since," you need a perfect tense:

Those were the first kind words he had heard since beginning his chastisement.

Those are the first kind words he has heard since beginning his chastisement.

(2) Peter explained it well. I would like to add something, though. Here's a similar sentence where the past perfect is helpful:

We had just begun playing when it started to rain.

The past perfect is helpful when there are multiple things in the past, and you want to position the two things in slightly different places on the timeline. I recommend that you practice drawing actual timelines when thinking about these sorts of sentences.

(3) All three of these sentences look good to me. I could go out of my way to find some subtle differences, but most people reading a news article quickly wouldn't notice a difference.

For each version, I'll quote your sentence, put an explanation in parentheses, and then give a simplified version that will hopefully make it easier for you to see what's going on.

(a) One of the young men who had been injured in an attack on our supply lines was a laborer on the construction site. (His injury occurred well before he started working at the construction site.)

A young man had been injured in the attack, and he was [now] working at our site.

(b) One of the young men who were injured in an attack on our supply lines was a laborer on the construction site. (This one is more ambiguous.)

A young man who was injured in an attack worked at our site. (Without context, we're not sure when one thing happened in relation to the other thing.)

(c) One of the young men who were injured in an attack on our supply lines had been a laborer on the construction site. (He had worked previously at the site, prior to being injured in the attack.)

A young man who had worked at our site was injured in an attack.

Helpful guidelines:

• If you have two things occurring at two different points in the past, you'll probably want to use past perfect for the more distant thing.

• To be sure of what you're doing, change your point of view. Put the narrator back in time, so he can describe the action using the present tense, and perhaps the present perfect. When that sentence looks good, then shift the present tense to the simple past, and the present perfect (if that is a feature of your sentence) to the past perfect.

  Related to what I just explained: when you come across some use of the past perfect in your literature reading, try rewriting the sentence by doing that shifting. This will help you get more comfortable with perfect tenses.

• Learn the "since" pattern by memorizing some paradigm sentences. When you want to construct a "since" sentence, try to follow one of those paradigms.