In the case of rust, there are a lot of chemical similarities between it and hematite (though contamination with iron hydroxides might be a problem), which might (theoretically at least) make it potentially suitable for smelting into pig iron. I don't think any existing industrial processes do this, though.
It's not a problem to remove rust from iron. Just heat it in a low oxygen atmosphere, and add carbon which will react with the oxygen in the iron.
You do need to carefully control the amount of carbon though.