Excellent. I feel very lazy for not just using Google for that question...
I believe that it is more common to use the past tense in Swedish, for example "Det var inte det jag sa", whereas the present tense is more natural in English: "That's not what I said". In other words, I think "Det var inte vad kungen sa" should have the most natural translation "That is not what the king said".
It and that are both accepted answers. For the tense, we'll try to keep the translations as straightforward as possible, thus preferring was or var here.
Absolutely, but "type what you hear" exercises have a bug where only one translation can be accepted. It's very annoying.