It means to join in and sing the same thing as someone who is already singing. It's often part of a coaxing invitation. The phrase is often used when a singer is performing in front of an audience, singing alone, and then invites the audience to join in and "sing along" with them on a song. "Along" carries the idea of singing at the same time, in synchronization, probably in unison. There is also a noun, "a singalong," which means a group singing event in which people are invited to sing along with a leader. In the Beatles' song, "Sergeant Pepper's Lonely Hearts Club Band," there is a good example of use: "I don't really want to stop the show, But I thought you all might like to know That the singer's gonna sing a song, And he wants you all to sing along." In the 1960s, bandleader Mitch Miller had a weekly television program called "Sing Along with Mitch." He really wanted people, in their living rooms, to sing along with the program on their television set. The chorus--"the gang"--sang simple songs in a simple way. It would be natural to say "When I was a teenager, I loved [so-and-so]; I used to buy his records and sing along with them."

It can mean 2 things, depending on the context. It can mean sing with me It can also mean to sing along as the song is playing.

Yeah “sing with me” or in a more broad sense “sing with an ongoing song”

Yes!

Yes. For example in children shows the character will sing a song and they will say “sing along”. This tells the viewer to sing with them in the cartoon