"I am drinking my tea."
Translation:Piju svůj čaj.
Not in a simple sentence like this.
You could use "můj" for a very strong additional emphasis, usually when emphasizing contrast. For example, you could say "Piju můj čaj, ne tvůj!" while replying to your friend who's accusing you of stealing his cuppa.
In any other scenario, remember the simple 'svůj indicates possession by the subject of the clause.'
It can, but this particular word order will only work when you strongly stress piju. And that is quite artificial here. Like if someone was suggesting you are doing something else with your tea and not drinking. And you say I am DRINKING my tea.
But anyway, it IS accepted. If it was not accepted for you, it might be the infamous grading bug.