Mafia 83. Doctor Who: Aliens in London

Will the role of the executed character be indicated during the execution?

Approximately the same as in a newspaper – I won't say it directly, but you'll be able to understand it from the description.

Will they be allowed to say their last words?

Only as a form of creative expression, like a regular in-game post before the execution, and, of course, within the usual game rules – without revealing roles or other statuses.