If you don’t want to buy a new grinder, you could try running the coffee through a coffee filter afterwards. So you grind the beans, let it soak for however long, and then run the coffee through a coffee filter. I use a Chemex to make coffee sometimes, so I use that but anything will work. I’ve put a filter in a funnel and used that.
This will catch the sediment, in my experience it has taken a while to filter through.
Same. I have been spraying some water in the coffee beans before grinding, about 0.5-1g (two sprays from a water bottle) prior to grinding and have had no issues.
If you have build up in the chute, you can try tapping the grinder prior to removing the container.