Also, a common startegy is suspending the whole deck and unsuspending some cards (usually with a certain tag) whenever you’re ready for the next batch.
As for your third question, that sounds like your card design could be improved.
First, you should use separate cards for separate information, that’s the minimum information principle. Why not have one card where you see the Kana and have to recall the reading and one where you see the romaji (or hear the reading) and have to draw the kana?
That alone should be enough so you don’t have to think about what kind of information you have to recall. (There are plenty of other reasons why this is the superior approach, by the way.)
But to further help with that, you can give each template a distinct look, e.g. a different background. You will soon be able to recognise what is asked of you without thinking.