Two questions
 

The first one is: what does 'boogie' mean?
And does 'blue' mean sad?

Thanks.

As far as I know, "boogie" means to dance or to party. It might have several meanings though.

What do you exactly mean by blue?
Like "out of the blue"?

I'm blue. = I'm sad.

Out of the blue means from out of nowhere. In this case the blue refers to the sky.

To be blue definite definitely means sad, but in some contexts it can means severely lacking oxygen as in symptoms of cyanosis.

OK, and where do they come from or why do people started to say these expressions?

Well, "the blues" is also a musical genre that originated toward the end of the 19th century mostly in African-American communities of the deep south; it is one of the sources that contributed to jazz, rhythm and blues (also called R & B), and rock and roll. "The blues" songs often tell stories of misfortune and unhappiness.

OK, I understand. Thanks.

You may also here these expression:
I have the blues. (be melancholic)
The Blue refer to the soldiers from the northern states auf the US.
to feel blue = to be depressed
to arrive out of the blue = suddenly something's coming in
to look blue = to look cheerless
to make someone blue = to make someone sad

Ohh, how interesting, thank you!

I've also Heard that 'boogie' had something to do with American ancient culture, I don't know. Is it true?
Thanks.

The bogeyman (pronounced boogieman) is el cuco in Spanish-speaking countries.
I read in the internet the boogie is an derogatory term for people with sub-saharan ancestry, but I have never seen or heard it used that way.