Three people singing together is called a trio. It is also called like that for instrumentalists!
Choir
A sextet.
A duet.
Quartet.
Three people singing together is called a trio. It is also called like that for instrumentalists!
Trio
Choir
A sextet.
A duet.
Quartet.
two people singing together is a duet
The general term would be a quintet.
Audio engineer or sound engineer
The word you might be looking for is Kabuki.
Counterpoint
While there are several different types of singing without words, a common one is called scat singing. This type started in jazz and has transcended to many different genres.