I can agree that the combat music should end with the fight and not persist on the inventory screen. This will be changed with the next update.
We like to offer people a lot of control on how the game is played, but default to high accessibility. The game is meant to be played entirely with mouse or touch, but also be fully playable with just keyboard or controller. Certain design choices were made to accommodate this. We are considering adding an option to allow drag and drop support at some point, and have it partially implemented already. As for the tooltip remaining visible due to the item being selected, this is for keyboard/controller mode and we recommend turning it off in the Settings when playing with mouse. The option is called "Focus Tooltips" and is on the "Gameplay" tab. A tutorial will be added with recommendations, but it is a bit further down the to-do list.
We will be increasing the default speeds in the future, as we also play with both sliders at max, but also want to allow for not feeling too rushed for those who would prefer it.
The inn, where you heal and level up, is meant to be a town, with more to do. There will be a shop, and story events (including mini-boss fights), at towns. Adding story events is the next big update we want to finish.
Thanks for playing, and the feedback!