Does the 没 make it a question? And if so, how is it different from “你找不找到你爸爸了”
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Yes, adding the 没 at the end makes it a question. In this case, it is equivalent to "你找到你爸爸了吗？"
Without the 没, it would be "You found your dad". With the 没 makes it "Have you found your dad?".
It's kind of a shortened version of something like "Have you or haven't you found your dad?" (你有没有找到你爸爸？）(This is where the 没 comes from)
你找不找到你爸爸了 doesn't really mean what you would think it would ("Have you found your dad?").
Instead, this pattern (Verb + 不 + verb ... ) would be something like "你找不找得到你爸爸？”. This would mean "Are you able to find your dad?"
You can however say "你找没找到你爸爸？" if you want to use this form.
It's short for "你找到你爸爸了没有?" or "你找到你爸爸了还是没有找到?". The complete sentence should be "do you find your father, or not?". "没" here is similar as "or not" in English.
BTW. The "你" before "爸爸" is redundant in Chinese. "你找到爸爸了没" is correct. It is impacted by translation from western language. Even many Chinese make this kind of mistake too.
I think it's actually 了没 that works together, instead of the single character 没. 了没 can be interpreted as Have ... yet?. It works in the structure "verb + 了没". For example, 你吃了没(Have you eat yet?)，你去了没(Have you gone there yet) ...
Sometimes, we can omit 了. E.g. 看没？= 看了没？， 说没？= 说了没？
It's pretty common. It can probably work for any verbs.