Translation:He has not walked since he got sick.
"He doesn't walk since he got sick" would be a more accurate translation. People usually reserve the past tense for finished actions, and in this case, the guy's still not walking, so the present tense is preferred.
One of the accepted translations is "He does not walk since he became sick". So, is there any difference between "Ele não caminha desde que ficou doente" and "Ele não caminha desde que se tornou doente"?
"Se tornou doente" is very strong. It would mean he became sick in essence, permanently. You wouldn't say that.
But "ficou doente" is transitory, and the good option.
You could compare "se tornou" with "ser", and "ficou" with "estar" in this case.
Just don't say "se tornou doente". That's bad.
Sounds like tornou is a good word ff you're talking about a guy who changed into something bad. Would you, for instance, say "se tornou zombi"?
More commonly "virou zumbi"/"se tornou zumbi". (Turned into a zombie)
would ´´he has not walked since getting sick or since he got sick´´ be an acceptable translation?
Why does "que" show up after "desde" in this example, but not in some others?
You would expect a time adverb after desde (as in desde ontem), but instead, there is an entire clause (with a verb - FICOU doente).
In those cases, you add a conjunction ("que" or "quando")