‘The Prince of Egypt’ depicts an Egyptian noble dwelling opening up to the Nile (the water literally travelling into a room where it finishes at what appears to be marble steps). Have such dwellings existed in Ancient Egypt or other cultures?

I´m assuming you´re referring to the scene in which the basket containing Moses is found by an Egyptian woman.

This particular structure seems to be more inspired by temple-architecture rather than domestic buildings. Most dwellings, noble or common, tended to be constructed with adobe or mudbrick as the basic materials; which does not fare well when in constant contact with water. Marble was generally reserved for royal palaces and temple complexes as it was exceedingly expensive and had to be transported from marble quarries located in Upper Egypt. In any case, noble residences tended to be located within the city limits; where they would usually consist of an enclosed courtyard centered by a multi-storied building surrounded by smaller structures used for storage. The waterfront was usually where farms and irrigation canals would be located. Noble residences did exist outside of the city itself, but would usually be situated further from the waters edge, especially in the delta of Lower Egypt. Mainly because of waters corrosive properties with regards to the mudbrick/adobe during flooding.

A bit further upstream, there were structures close to the waters edge though; but not in the way depicted in the film and they were not dwellings, but temples and royal palaces.

The Temple of Luxor was situated directly adjacent to the Nile, but does not seem to have had any passage connecting it to the river. The nearby temple of Amon-Ra at Karnak had two canals leading up to the temple itself, but one formed an artificial harbor and the other supplied, via pipes, two enclosed water basins. The royal palace at Malkata also lay on the riverfront, but had no inlets into the structure. In fact, the only Egyptian temple, which I can think of, with an opening close to or directly at the river front would be the temple of Abu Simbel. In many reconstructions, the temple entrance is shown as flooded or close to being flooded during the flooding of the Nile. For most of the year however, the entrance would not have been inundated.

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I ask because it seems like it could be a hazard (waterborne disease, crocodiles etc.) and difficult to execute architecturally. While I know the last point may seem laughable considering we are talking about a culture that literally built pyramids, I still find it hard to visualise given the inundation cycle and the difficulty that comes with building in such conditions.

The Egyptians would have certainly been able to build such a structure, however (as you yourself pointed out) it would have been foolish and very expensive to do so. Even if they would have managed to keep potentially dangerous animals out and used waterproof stone and granite in the construction; the water level would have still remained unpredictable during the flooding.

Even when I consider a building in another location, perhaps opening to a river or the sea, I still don’t know how this would work.

Indeed. An (artificial) lake would seem to be the most feasible. The sea would bring in the problem of tidal flow, whereas a river would have to be incredibly constant in its waterlevels.