Waterways and terrain placement

I admit my first response was a chuckle of amusement, but on thinking it over your question does raise some interesting possibilities.

Since you have specified a hill or marsh (area terrain) being placed in or near a waterway (linear terrain), the 1 BW gap restriction does not apply. However there are some more general guidelines on page 6 of the rules that might help. I think "...varied and realistic terrain is essential for interesting battles." and "The types of feature that can be used depend on those of the terrain in which the defending army historically normally fought at home." show that the author had in mind the creation of a reasonably realistic battlefield. So, in the absence of any rule to the contrary, all you need to do is apply a test of realism.

I'm sure we have all seen real examples of hills that extend up to or into deep water, both on the coast and inland, so Q1. and Q2. pass the reality test.

A hill placed entirely in a waterway (i.e. an island) would usually be irrelevant for game purposes, but again, there is no reason why your opponent should object, especially if you are trying to represent a real location. I can imagine a scenario where a bridge or ford between an island and a river bank might be an important tactical objective. Reality check passed.

Finally, are waterways sometimes shallow and marshy? Absolutely! Are there any real examples of BUA's located in rivers or off-shore islands. Yes. Have you ever been to, or seen photos of Mont St Michel? It has been assaulted or besieged several times. Of course, you would also need to represent the causeway, but that is really just a continuation of the road leading there. It might be interesting to simulate an attack under the pressure of a rising tide. I'm sure that, with a bit of reflection, several other examples may emerge. The siege of Venice perhaps?

In any event, I don't think the issue is as silly as it might seem. DBA has a great ability to simulate real battles in a simple game format and your question highlights the flexibility of the game.

Northey Island and the causeway are a very good example.