Finishing the story doesn't prevent you from doing any quests.
After finishing the quest to get the grenade, you should be able to go upstairs and find a treasury. The invisible woman is long gone by the time you come back with the grenade.
All events for main characters are explained step by step in the walkthrough. I don't now what step you're on, but you should be able to find what you're missing for "Vampire's past" there. Library Exploration is a quest after Vampire's past.
The royal invitation requires that you finished all previous paperwork on your desk and that you had the second political meeting with Begus. Talk with Theremis in your throne room to arrange a meeting.
Neya appears in an event in Kagabangui when you go up the stairs on the right side of the city, but it requires that you've had the first sex scene with Vampire.