Is my private data on my old iphone truly erased when I reset it before turning it in for a trade in?

Is my private data on my old iphone truly erased when I reset it before turning it in for a trade in?

Yes, if you follow these instructions:

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Are all my old passwords that were saved on my phone accessible by the new person who gets it?

There is nothing on the phone "to get" if you follow the instructions.

Has anyone ever been hacked by a new user getting "inside" data from the supposedly "erased" old phone?

No, but keep in mind that you can always find articles on the Internet claiming to prove that the earth is flat, so you can probably find something if you waste enough time looking.