In the movie "Grease" do the actors and actresses actually do the singing?

Yes

Yes, indeed.

https://en.wikipedia.org/wiki/Grease:_The_Original_Soundtrack_from_the_Motion_Picture

Years later, on "Inside the Actor's Studio", John Travolta spoke a bit about acting in musicals. His advice to students began: "First of all, don't think of singing in any way differently than you think of speaking. The songs are just another way of delivering the script, dont sing differently than you speak..." It is that advice that I've tried to keep in mind ever since as a composer, a librettist, and a singer.

Yes, Olivia Newton John was a famous recording star prior to her acting in the role of Sandy in the musical film Grease. John Travolta used his acting clout and fame to parlay a record deal and released an album and scored a seminal hit with the song "Let Her In."