"Peter fights next to the city."
Translation:Péter a város mellett harcol.
Only slightly; IINM word order determines what the emphasis is placed on. So, "Péter harcol a város mellett" would mean "Peter fights next to the city", whereas "Péter a város mellett harcol" means "Peter fights next to the city". It's not a huge difference.
Am I right, native speakers?
Yes, close enough. :) But emphasis can also play a major role. Depending on what you stress, the same word order could mean different things:
"Péter a város mellett harcol" - this is the most neutral order. "Peter fights next to the city.
Now, with extra emphasis, the same sentence:
"Péter a VÁROS mellett harcol" - next to the city, not next to the river
"Péter a város MELLETT harcol" - on the side of the city, not against itt
"Péter a város mellett HARCOL" - what he does is fight. not pick flowers
I haven't emphasized "Péter" yet. For that, I need to change the word order:
"PÉTER harcol a város mellett" - It is Péter, not somebody else, who fights.
You could also emphasize it like this:
"Péter HARCOL a város mellett" - he fights, he doesn't just talk.