Ok, for the first one,
- "The Doctor is a tall, old and smart man." is the correct way in British grammar.
For the second one,
- "Trust me. I'm the Doctor." is correct, but there are several variations that you can see at Thread:131641 (which is actually the one I meant to link above).
For the third one,
- Missy is the Master. (TV: Dark Water) is correct, not for grammar reasons but because at some point it was chosen by the wiki community to do it this way. Sometimes we choose policies that aren't necessarily grammatically correct, such as Tardis:Quotation marks, where technical reasons force us to use the American style despite the wiki in general using British grammar.
Hope this helps, let me know if there are any other questions.