Did and European nations try building new Roman-style aqueducts?
It bears noting that while people picture arched water-bridges when they think of Roman aqueducts, it should be stressed that these are just the most photogenic elements of the system. Far more of the Roman aqueduct is underground - and so is the Medieval aqueduct. I have a post specifically concerning Medieval aqueducts here.
How else did they handle the growing water demands of cities?
As the Medieval ticks over into the Early Modern, we start seeing water-engines. I have a post specifically concerning Early Modern water-engines here.
While we're here, we may as well do a spot of myth-busting, just in case anyone walks in with that "Medievals didn't drink water" business.
As always, should you have any further questions, please don't hesitate to ask!