I notice that contests go on during the fest, but I can't seem to figure out how to enter for a specific one? Do I just do the stuff and it will place me automatically, or do I have to sign up?

for the forum contests, you just follow the rules, for the Boards, they're automatic:

Nurturing board- you get 1 point for every eggling/hatchling you nurture to the board of that pet's species (eg. nurturing five aeridini eggs gets you five points on the aeridini nurture board.)

Battle Board- each pet in your team gets a point for its species board for each enemy you defeat in the Zone.
So a team made of a Zolnixi, vulnyx, and bulbori beating a team of three enemies would get you 3 points to each of Zolnixi, vulnyx, and bulbori boards.

Two vulnyx and a griffi as your team beating three enemies would get you 6 vulnyx points and three griffi points.

A team of three zolnixi beating three enemies would get 9 points on the zolnixi board.

Okay, that makes much more sense now. Thank you!