"Why he shouldn't smoke" is a content clause with an interrogation. It's not a full sentence and not a question. It could be used as part of a sentence, or as the title of an essay giving a list of reasons.

"Why shouldn't he smoke?" is a question. Literally it asks for the list of reasons, but it could probably be understood as a rhetorical question. The person saying this doesn't expect it to be answered because they imply that it has no answer.

So these are almost opposite in meaning. "Why he shouldn't smoke" would be used as a title by someone with lots of reasons. "Why shouldn't he smoke?" would be used by someone who thinks there are no reasons.

Likewise, "Why they shouldn't have a choice" is a content clause (not a sentence) that could be used as a title to a video giving reasons for them not to have a choice. But "Why shouldn't they have a choice?" is a rhetorical question that could be used as a title for a video clip that suggests that they are no reasons for them not to have a choice, and saying that, therefore, they should have a choice.

Now the implication is different if the question is asked as a genuine question. If someone says "Why shouldn't I smoke?" as a genuine question, it may be because they think that there are reasons for not smoking, and want to know what the reasons are. Or it can be rhetorical, as above. You can't tell if the question is rhetorical or not from the syntax, nor even from the intonation, but only from the wider context.

"Why he shouldn't smoke" is a content clause with an interrogation. It's not a full sentence and not a question. It could be used as part of a sentence, or as the title of an essay giving a list of reasons.

"Why shouldn't he smoke?" is a question. Literally, it asks for the list of reasons, but it could probably be understood as a rhetorical question. The person saying this doesn't expect it to be answered because they imply that it has no answer.

So these are almost opposite in meaning. "Why he shouldn't smoke" would be used as a title by someone with lots of reasons. "Why shouldn't he smoke?" would be used by someone who thinks there are no reasons.

Likewise, "Why they shouldn't have a choice" is a content clause (not a sentence) that could be used as a title to a video giving reasons for them not to have a choice. But "Why shouldn't they have a choice?" is a rhetorical question that could be used as a title for a video clip that suggests that there are no reasons for them not to have a choice, and saying that, therefore, they should have a choice.

Now the implication is different if the question is asked as a genuine question. If someone says "Why shouldn't I smoke?" as a genuine question, it may be because they think that there are reasons for not smoking, and want to know what the reasons are. Or it can be rhetorical, as above. You can't tell if the question is rhetorical or not from the syntax, nor even from the intonation, but only from the wider context.

Asking "Why should they have a choice?" rhetorically would imply the opposite. It would suggest that there were no good reasons for them to have a choice, and so they shouldn't have a choice.

When do you think children should be able to choose which subject to study at school?

Why should they have a choice at all? All the subjects are important and if children can choose to drop some, they will miss out on some important learning.

Do you really think so? Let me tell you why they should have a choice. If children don't get to choose which subject to specialise in, they won't be able to learn in depth. And they may be demotivated by studying a subject that doesn't interest them.