In the Lakeview Guild Hall I accidentally spammed through the specific Witch Academy student's request text & cannot find the Demon Nursery she's talking about.

Am I supposed to re-visit to any of the pre-existing one{s} or has a new one formed?

It's the dungeon at the beach, there's a path that's blocked off before the request. To avoid making another heading, I can't get the slime research quest to trigger at all.

Thanks!

Try going slightly right of Lakeview, then straight down to those 2 rings at the mountain pass (with a small branched river in between them). The upper one will trigger it, but another indicator that you're in the right area is that the bottom one will bring up a text string suggesting you go to the upper one.