"화장실에 남자가 있습니다."
Translation:The man is in the bathroom.
Not really.. It's not just a matter of word order. For example, this cannot be an answer to- "남자는 어디있어요?" In this, the emphasis is on the whereabouts of a certain man. Although if the sentence had been "화장실에 있습니다, 남자가.", it would have the same meaning as "남자가 화장실에 있습니다" Now, the actual sentence could be an answer to a question like- "왜 화장실에 가지 않아요?" asked to a person who is standing in front of the bathroom without going inside.
Word order is very fluid. The order doesn't matter much to the translation (as long as the verb is at the end. That's a hard rule). The difference is the emphasis. So by putting the 'in the bathroom' first, someone who says this is emphasizing the location of the man, not the man himself.
Think of it as an answer to a question.
"Who is in the bathroom?" Vs "Where is the man?"
Is 화장실에서 acceptable? I learned somewhere that it meant 'inside' of something.