We do have upload settings in themes, but there’s still some refinement we need to make to those. So, for now, the answer is still the same as described above. Upload your images in a staff topic and grab the URL.
It won’t. Large images get resized, but the original is always preserved if you click on the lightbox. Small images are uploaded as-is.
That’s not possible, and even if you manage to find a way to do it, it’s not recommended. Discourse creates records for uploads. At best, you end up with a mess. At worst, you end up with a broken site.
Long term, we can potentially support type: upload for badge images and have a radio input that lets you switch between the icon picker for icons and the upload setting for images.