1.  Yes.

2.  The 'patches' are called flap valves, and yes, the air from the
bellows is evacuated through them.  They must create a tight seal on
the intake phase of the cycle in order to have a vacuum.  You must glue
down the ends of the valves, or replace them if the leather is too
porous to make a good seal.

3.  If you repair the flap valves as above, the organ may work without
replacing the bellows cloth.

4.  The rod connects the bellows to the crank, so when you crank the
organ it operates the bellows in addition to turning the cob.

Larry Lobel
Virtuoso Piano Service
Petaluma, CA