In a play, the dialogue is set in quotation marks?

Answer 1

Not usually. This depends upon the editors of the edition you are using. However, the standard publishing format for a play is to have the character's name indicated in the left margin, and then what they're saying follows a colon. Anything not spoken in a play (e.g. stage directions) is typically set in italics.

Example:

Ceasar: Even you, Brutus?

Caesar dies.

Cicero: Nice work, Brutus. Way to save the republic.