How can I automatically download all images from all imported posts, place them on my new host, and replace all the links

There are plugins that do this, e.g. Auto Upload Images (found in this article). I haven’t tried it myself to recommend it.

You’re migrating from BlogEngine.NET. There is also an old BlogML importer plugin to migrate directly from BlogEngine.NET (which produces BlogML exports), but the copy in the main WordPress directory hasn’t been updated in years and is no longer available to download. There is a fixed up version here: http://spacefold.com/colin/morethanfour/2020/08/06/migrating-from-blogengine/ however the process does also require manually fixing up image paths.