Translation:The doctor makes the professor healthy.
"make healthy" works in German, but does it actually work in English? I know this sentence is supposed to emphasize that "sanus" in this case is an adjective
2 accusatives? Or it is literally "the doctor makes a healthy professor"?
More like the latter. "Sanum" is the adjective for "professorem". The sentence basically means, "The doctor heals the professor". Sanum facere = to make healthy -> to heal.
Curiousity: could this also say: "the doctor makes the healthy professor?" It's almost as though 'facit' takes two objects in the given translation (taking a professor, making him healthy), whereas it looks at first glance like the accusative 'sanum' is simply supposed to modify the direct object.
your sentence isn't a wrong translation technically, but it doesn't really make any sense. in latin, we have a thing that is called douple accusative, and that's what's happening here (i think) - so yes, two objects in the same case and numerus because the adjective /does/ relate to the noun, but isn't a direct modifier