Yes, jpg, jpeg, png or gif. If it's there, it's used, if not, then knots will try grab a screenshot of the video with ffmpeg. For album art, you can use the "Fetch missing album covers" button. But you should first edit your album and artist tags so that there are no duplicates. Knots automatically applies the same image to each song in the album so the image is stored only once in the database.

Nope, you have to set them manually for categories, tags and values for now.

I do use themoviedb.org database and they do have images too, but their aspect is little wrong to my usage so I haven't implemented an automatic fetching, sry.