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1. Is this sentence correct:


"In Carnival, people dress themselves in fancy costumes."



2. And would it make sense, OR MEAN THE SAME AS ABOVE, if it was said:


"In Carnival, people fancy themselves."



3. Finally, what do you understand by a 'fancy party'?


And what would you call a party in which people dress fancy costumes?

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Christine Christie1. Is this sentence correct:
"In Carnival, people dress themselves in fancy costumes."

Yes, provided we accept "In Carnival" without any article, which people seem to.

Christine Christie"In Carnival, people fancy themselves."

This means something completely different (at least in BrE). To "fancy oneself" means "Have an unduly high opinion of oneself, or of one's ability in a particular area" (https://www.lexico.com/en/definition/fancy#fancy)

Christine Christie3. Finally, what do you understand by a 'fancy party'?

An elaborate or sophisticated party.

Christine ChristieAnd what would you call a party in which people dress fancy costumes?

A fancy dress party.

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Here's the broad idea.

fancy means elaborate, not plain.

eg Most people wear fancy clothes when they go to a wedding.


fancy dress is an idiomatic way of referring to the amusing and whimsical clothes that people, usually children, often wear at Halloween. eg monsters, witches

Look here. https://www.google.ca/search?ei=kWZmXdPwDM3wsQXN_6foDQ&q=halloween+costumes+for+couples&oq=halloween+costumes&gs_l=psy-ab.1.9.0i131l4j0l6.14978.19743..33029...0.2..0.114.1806.23j1......0....1..gws-wiz.......0i71j0i13j0i13i30.yIa6ZJ-yy_c

Now let's look at your questions.

Quote

1. Is this sentence correct:


"In Carnival, people dress themselves in fancy dress costumes."



2. And would it make sense, OR MEAN THE SAME AS ABOVE, if it was said:


"In Carnival, people fancy themselves." No. This means that people think they are special.



3. Finally, what do you understand by a 'fancy party'? an e;egant and expensive party


And what would you call a party in which people dress fancy costumes? a fancy dress party

Clive