Learn English – Comforting/encouraging English idiom meaning ‘it’s not that bad’/’it’s not all bad’

In the context of the lyrics I interpret it as meaning that she shouldn't be too naive and think that just being nice (smiling to people) will mean people won't try and use her. She has to be aware that other people are not always good and should look after herself because "there's a lot of bad" out there.

Of course song lyrics can often be interpreted in different ways so other people may disagree with me on this.

In English, there is an understanding that a double negative equals a positive.

Your example:

Nothing bad wouldn't happen...

means everything that is bad would happen. Why? No thing which is bad would not happen.

The idiom is common in English as well. Often it's expressed either way, it's ok, or either way, it's good.

"Bad publicity or good publicity, it still exposes people to our mission. Either way, it's good."

If yes, ok; if not, nothing bad will happen, right? (punctuation edited)

is fine, as you did not use a double negative here. The not is separated from nothing. For a more common expression, make the last part a positive instead of a non-negative:

If yes, great; if not, it's still good, right?