I have two confusing things on my mind.
1. Some of the girls when they rape you will make a heart effect upon climax, this heart effect generally denotes additional H-move opportunities (the first boss did it to denote her yuri attack). The mother slime girl also does it which I think is key to getting her present.
2. At the top of the tower area with a twintailed girl that has more health than usual, she has a special blue heart move (denotes that it occurs when you have a blue sash), and this move consists of a blue ring that when touched surrounds your character in blue energy. If you don't struggle out of it, you will be abducted into a spaceship full of the twintail girls... there doesn't seem to be a point to this.
So far by my experience present drops seem to be random, whether the girl drops presents or not can be seen in the dictionary. I haven't noticed the heart part but if there can be a confirmation that would be nice.
Certain monster girls have blue hearts next to their regular hearts, I believe this is not an extra H scene but a new way for interaction with the girl, the ones with this that I know of are the lamia(aka stone lamia) and the lilith on the top of the tower. The lilith takes you to their ship(which I think sth will be added in future patches). And the lamia interaction, I think it has something to do with the stone statue girls in some maps and in some bath houses, this may be already in the game or will be added in the future.
An NPC has hinted sth about extracting poison but I haven't figured out the entire thing yet
Hearts that are dots (not interactable) I think have sth to do with the area or a very specific situation(eg. The black haired twintailed girl kirin has a scene only available at the city with an old-style jukebox, the girl herself had a different naming than the original Kirin version), which girls do shota or yuri they made it very clear already