Dear Park, Yes, you are right that "to show sb out" is a phrasal verb. It means to lead someone to the exit. The verb in the second is simply "to show".
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park sang joonI think in #1, "show out" is aYes.verbal phrasephrasal verb.
park sang joonwhat role "the way" plays.'the way' is the direct object of the sentence. 'out' modifies 'way'.
Michael Chambers Teaching English"Exit" is used in the same way in the UK as the USA, and is also very common in the UK - probably more so than "Way Out". MichaelI think my information must be out of date then.