Not NTR per se, but yeah, unless the player pursues a relationship with her, she and Gouki will end up together. Hana really can't stand Nao and Azar (thief and blood magus girls respectively) so spending time with either of them gets points off her romance.
In the new update I will have a lot more content with Hana (and chances to romance her/h-scenes), so look forward to it. For the version you're currently playing though: I intentionally put few romance events in the first floors (there are 13 total) to give a better sense of pacing. Your chances will go up the higher the floor.
As for the locations, I've tried to make potential romance sub-paths be more on less along the player's path for the main story, so you can't miss them