1. I am working on a setting that will increase the animation speeds drastically! Other people have also said similar things.
Also, there is a restart run button! Settings Menu -> Other -> Reset Run. You can select it and it will replay the level without having to go through the main menu.
2. I am also working on that feature as well! I was thinking of making it much more simple with a "B" saying it's been bought for non-accessories, or a "1/3", "2/3", or 3/3" for accessories. I'll experiment with your idea of showing if an item is equipped/purchasable. It's not something I thought of before, but it sounds like a great idea!
3. I will add this! It should be easy given that it already works with touchscreen devices in the same way.
Thanks for your feedback!