1) The translator missed out/left out the difficult parts.
2) Why did you miss him out/leave him out of the group?
3) Remember not to miss out/leave out any words in the exercise.
Do they always mean the same? Or is there a slight difference in the meaning?
Because that isn't what "miss out" means. It means you have lost an opportunity to do something.
miss out - Idioms - by the Free Dictionary, Thesaurus and Encyclopedia.
I don't have a problem with the first or third. "To miss out" in BrE can mean "to omit".
You missed out all the articles in your paragraph.
The translator missed out an entire sentence from that text.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.