1.)  The shafts are angled such that water from rain or melting snow can be channelled into rills and thence into drains -- possibly thence into cisterns.  Drainage is managed by virtue of a large, subterranean lake beneath the mountain -- water is chanelled into that lake which presumably drains into rivers flowing into the Anduin. 

2.)  Beats me. 

3.)  I guessed defensibility as well. 

4.)  There were clearly other exits: the Endless Stair was one.  There were probably dozens of other hidden outlets and the like. 

5.)  There are plenty of natural rock formations which function as bridges over chasms -- and stand for many centuries.  E.g. a brook flows down a mountainside.  Slowly it excavates a ravine.  However, lying directly across the brook's path is an outcropping of extremely hard, but not very thick (measured vertically) rock.  Because the rock erodes very slowly, the brook digs under the rock.  Centuries pass, and the brook has excavated a deep ravine spanned by a natural bridge.  The bridge over the chasm in Moria was not natural, but my UUT is that it was composed of a single slab of hard stone fitted into sockets which had been hollowed out on both sides of the chasm.

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All that is gold does not glitter,
Not all those who wander are lost;
The old that is strong does not wither,
Deep roots are not reached by the frost.
From the ashes a fire shall be woken,
A light from the shadows shall spring;
Renewed shall be blade that was broken,
The crownless again shall be king.