1) No; the blank save file setting applies to startup as well; when a save file is not detected for loading, it will create a blank save based on the setting. Changing the setting while the program is already running will load a new blank save, out of convenience.
2) No; shortcuts are not tools. The tools menu is already quite cluttered, and is where Plugins normally add their actions. "Options" are different choices the user can make, and providing information about different options of doing things (via hotkey, shortcuts, etc) is by definition an option.
3) https://github.com/kwsch/PKHeX/commit/6bb2612059edc014d6e448c929bb08d985e04ab7
4) Derived properties aren't normally interactable. I've added user interaction help to dropdown when clicked. https://github.com/kwsch/PKHeX/commit/a221a27074aacbb293295bc993fbe70d42d6c453
5) Too many buttons is visual clutter. Things are clickable.
6) Not worth the effort. Translations are heavily neglected for certain languages, and this would increase visual clutter. If people don't know what a label or icon is, they can search the forums or wikis.
7) No. Calculating the amount of occupied slots for a box and updating it on every get/set operation results in tangled logic for very little value added, if any.