No, it is necessary. The problem in that sentence is the comma. It needs to come before down, not after.

Yes you can omit it. The problem is the use of the relative clause here, "....which sewage ran down". The word "which" must be replaced with "whose". Whose denotes possession. If you retain "down" you must alter it by saying" ......is a maze of narrow alleyways that run downhill or is a maze of narrow alleyways running downhill. I would prefer the latter as it then flows with the whole style of writing

Andy and Wendy. I will rewrite the whole sentence: The Old Town, medieval in style, is a maze of narrow alleyways running downhill whose sewage once ran freely. Or The Old Town, medieval in style, is a maze of narrow alleyways that run downhill and whose sewage once ran freely.

I think a previous responder is confused by DOWN. It doesn't always literally mean downhill. You can just say are running down the street--and it could be a flat street. That said, your original sentence actually works, except for moving one comma: The Old Town, medieval in style, is a maze of narrow alleyways, down which sewage once ran freely.

🔴 The original question was: “My question is: what's the usage of "down"? Can I omit it?” I even had to google a similar phrase for Wendy: “to walk down the road: to stroll down the street, to walk on the road, to travel by foot along the lane.” “to go down the street” = “to go along the street” So, you can NOT omit it without changing the sense of this sentence. You can only substitute the word “down” with “on” or with “along” It is not about any slopes of any hills (even it is difficult for us to imagine))) It says that it was common and acceptable that the narrow streets of that town were used instead of the sewage pipes. If you google “sewage meaning” you get: “waste water and excrement conveyed in sewers.” That definition was absolutely incorrect for the Medieval Towns. The town streets were those sewers. That’s why the liquid was conveyed not inside of any pipes but was freely flowing (“running”) along the streets (“down the streets”). Even without any hills, every street is built with a minimal gradient for removing the rainwater. Though, it is not customary to use them as sewers anymore… ))) So let’s make a little quiz – everybody can choose TWO sentences with the closest MEANING: Wendy 1) ▶ The Old Town, medieval in style, is a maze of narrow alleyways, down which sewage once ran freely. Andy 2) ▶ The Old Town, medieval in style, is a maze of narrow alleyways, which served citizens as sewers. Mark 3) ▶ The Old Town, medieval in style, is a maze of narrow alleyways that run downhill and whose sewage once ran freely. P.S. 😜 People with an architectural or historical background have two voices! 🤣