Bunco questions

We picked up the game and tried learning it tonight.

As I understand it, there’s the “bunco” (you’re in round 1, you roll three 1’s for instance) and the “bonko,” where the three of a kind doesn’t match the round (you’re in round 1 and you roll three 2’s, for instance).

I couldn’t tell from the directions what happened if you rolled a bonko. We improvised (?) by saying ok, we’ll give five points for the bonko, but you didn’t roll the designated 1 for the round (in the example above), so that’s the end of your turn. Correct?

Second, as we understood it, you’re supposed to pick a number for the fuzzy die. Is it just a random number? Do people take turns picking it?

Third, when you designate a number, that fuzzy die gets handed around. That’s the long and short of the “reward” for hitting that agreed upon number, right? There are no points for it—but it would count for a win if you end up with it at the end, right?

Finally, why does the score keeper always start the round? That seems like an unfair advantage.

I’m pretty sure that whoever rolls a bonko keeps rolling until they don’t score anything on a roll (or the round ends).