From what I found out, you have to watch the piss drinking scene for the second scene, and the third requires you to buy an item from the secret store, she can be found in the area where you first encounter her, disguised as a sunflower.
1. You need to view the event about hikari & mom where you eat dinner at her place, that requires you to buy the mushroom(matsutake) from the secret shop first.
I don´t think it´s the sex ticket game, that should be the cover of the comic kings game. It´s about a boy who can do anything he wants.
The Japanese village/Wa no Sato should have a npc in the Gym area, talk to them and receive an item, the option to give Rumi the item should appear the next time you talk to her and battle will be engaged
Outside Central Tower, there's a blue & yellow colored flame with her icon.
This area.
In Harbor Town cave, on this particular grass only.
I bet you can figure it out, cause it's hidden. Goodluck
