According to MDN you can choose one of the following MIME types:
text/plain
text/uri-list
text/csv
text/html
image/svg+xml
application/xml, text/xml
application/json
So at the very least there's image/svg+xml, but that is pretty limiting.
Yes, but I don't think you can set the MIME type. So whatever you paste in would have to be smart enough to look at a text/plain clipboard data and figure out if it looks like an SVG (or whatever).