"Did you drink water?"
Translation:क्या तुमने पानी पिया?
Past tense verbs with a direct object should match the gender of the direct object not subject, right? So shouldn’t it be: क्या तुमने पानी पी? I’ve got multiple sources that indicate this would be the correct response.
You're right that it should match the direct object's gender, but पानी is actually masculine, despite the ी ending, so the solution "क्या तुमने पानी पिया?" in this case is correct.
Sites like Shabdkosh and Wiktionary are great for finding out the gender of words, if you're unsure of them. They've been pretty invaluable to me.
Kya can't come anywhere else. It has to be at the start
It can be omitted if you speak the sentence in an interrogative tone. It would be the same as changing the English sentence from Do you drink coffee? to You drink coffee?