how many notable tournaments (or tournaments at all) are their in a given timeframe?
I'm assuming you mean major tournaments, in that case? If so, there are about 2 or 3 major tournaments happening, with also 1 or 2 major lans happening in one year. Most tournaments are just minor ones that aren't really announced much.
How many entrants show to each tournament?
It is the same top teams that appear, most of the time, since the new teams don't get much of a chance to go out there.
Are matches streamed on Twitch, and if so, how many views do they average?
With the exceptions of the major tournaments (and lans) that have better setups like EndGameTV and InkTV that can get a couple hundred viewers, it's mostly just players that stream their perspectives, with their friends watching, like 10-15 people max
Have there been any serious sponsors?
I know there are a few teams that are sponsored, but not just for Splatoon, it's because the people that sponsor them cover other games too. Like they have a team for Overwatch, people that play fighting games and there's also a Splatoon team in there because sure why not, kind of deal.
How big is the prize pool?
With the excpetions of the major lans, there are little to no prizes for most tournaments. If they do it's like an artist that does a team drawing, but no money is involved in 95% of tournaments
Are there any big players?
Other than ThatSrb2DUDE, there isn't really anyone else that stands out and makes content in the competitive community, as far as I know.
How does the game stack up in numbers to "super-massive" games like League of Legends or "massive" games like Melee?
And as Reila said already, it's nothing much when compared to other games like Overwatch, LoL, Melee...
So it's doing okay but it's nothing too big right now, which fine, but if people want to get this game to be a big Esport, we need more content creators for Splatoon like DUDE