yes that's correct too. When describing a state (with an intransitive verb), it is mostly interchangeable for ています and ました.
I've written もう疲れたか - why is it possible to omit ましhere? Is it a less polite but grammatically correct form?
Yes it is dictionary form and is less polite than the polite form.
"Have you already gotten tired?"
Or "Did you get tired already?"
ました is no good?
You need to add "か" to turn it into a question