Kate's events and riddles are unrelated to Android.
For the solution, remember the four letters you gave in her four riddle sets. Enter them and she'll give you a big hint, aka how they're arranged. She did specifically say in the last set that you've gained knowledge that would lead to a reward very soon, after all.
Viewing post in Harem Hotel (18+) NEW UPDATE! comments
Right then, just seeking a direct spoiler for some fun riddles, that's fine. Itch.io doesn't seem to have a spoiler text thing so I'll just drop some lines so it has to be clicked on at least.
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vore
Like I said, each letter from each set. That's E - R - O - V. Enter them and she says "You're looking at things backwards". Enter them backwards, "vore". She'll explain immediately why she chose that word.