Conditional in the past: using present or preterit?

There is not a single, correct answer, because, when talking about events in the past, there can be conditions that continue into the present. The tense you use in this story can suggest different situations:

If they find out that he is still alive: This suggests he is still alive even now as this is being said.

If they find out that he was still alive: He might not be alive now, but he was at some point in the past, and that information might be discovered at any time, even in the future.

If they found out that he was still alive: Using all past tense places the possible death and discovery of the death completely in the past, without any real clue about the current situation.

There are even more tenses that could be used, for example: "They might be coming after me if they found out that he could be alive."

By the way, I might rearrange the sentence to be more fluid, and to keep the action of "come after me" closer to the effect -- "put the people I know in danger":

"If they find out that Kudo Shinichi is still alive they might come after me, and that will put the people I know in danger."