Rachel,
I don't know what happens if your king or queen die, or whether you can get a new king. My understanding is that the two parents have to stick around for the whole challenge, but I don't know if there's a specific rule.
Yes, you can collect plants, etc.
However, if you do 3 skill challenges before the next Reproductive Day, you can count only 2 of them. It's a pain with something like painting where your 30th painting might get you 3 skill challenges if it's also your 5th Masterpiece, but that's the way it is.