What order do they start in and when do they start becoming random when summoned?
The order starts out as EvilTaxi, Dakralai, jkeezer, Celeste, AgentBrand, Drazhar, and Hungry.
At this point, it either summons one of the Playerkai or goes on to the new CustomKai (Dale, Millennium, Vysaga, AzoJason).
When they're all done, it'll summon one random normal Kaiju that you haven't summoned before.
first the summoning info: "Before you can summon random Kaijus you need to beat the 13 custom Player Kaijus; Evil Taxi, Dakralai, Jkeezer, Celeste, AgentBrand, Drazhar, Hungry, McSmashy, Vysaga, AzoJason, Millennium, Dave and Shin Goji in that order. Also you cannot summon an old kaiju until all new kaiju have been defeated in your village." - taken directly from the enticement altar page
secondly there are a few small spelling errors in the page… (why they haven't been caught is beyond me, but probably due to priority of info over spelling.) …it causes sabatoge "sabotage" damgage "damage" to a random upgrade the village has. If a kaiju is not deafeated "defeated" by 7 days…
I'm sure every village has these same questions asked constantly about Kaiju, and indeed I even forget the answers myself a lot of the time. It'd be nice if we could just forever point to here for a quick reference.
Does attacking a crippled Kaiju give you tickets for the original monster drop roll?
Does attacking a crippled Kaiju add to the "damage done with Terri3" for your chance at that drop?
i believe the answer to both those questions is yes.