First of all, the Hungarian sentence is unnatural. I would never say something like it. The common form is "Az orvos most sétál", "Most sétál az orvos" or "Most az orvos sétál".
The given translation (the doctor is walking now) equals to "az orvos most sétál". Your sentence (the doctor is now walking) equals to "most sétál az orvos".
Is this a correct word order in English? Shouldn't "now" be at the beginning or at the end of the sentence?
The 'now' is free. It can be anywhere except between "the" and "physician". Having it at the beginning or end would be more common, though.
Shouldn't this be "sétálsz" instead of "sétál"? My understanding is walk=sétál and walking=sétálsz. Correct?
I am not sure that your phrase is correct in English. If you are doing something at the moment of speaking you have to use present continuous tense. Please correct me if I am wrong. However one says: -The doctor walks five kilometers every day.
Was accepted when I typed it like that. If someone tells me how to add a picture, I can show.