What does a dialogue consist of? I mean, what are these constituents called?
In acting, these are called lines
lines the words of an actor's part in a play or film. [NOAD]
Normally these are used in plural, but can be used to refer to a single line of dialogue.
You can say lines, in the sense of “the words of an actor's part in a play or film”. Example of use:
the problem with Jack is that, in the love scene with Rob, he couldn't say (or deliver) his lines with enough passion