Larry, (1) You are correct that the reservoir contracts (moves down) as
the vacuum builds.

2) The "patches" you describe on the exhauster bellows are flap valves
which exhaust the air.  They are supposed to be attached at each end,
and act as "check valves" allowing air to pass out of the bellows.
A similar set will be found between the exhauster bellows and the
reservoir.  You'll need to replace them all with new leather at the
same time the bellows cloth is replaced.

3) The old material can be removed by some combination of heat,
moisture, and physical means.  As there has been discussion of
techniques before, find that information in the MMD archives.  Also
in the MMD archives you will find discussion regarding the use of
hot hide glue for replacement of the bellows cloth.

4) The "wooden rod" you mention is the relief valve, which opens as
the reservoir fully closes.  It prevents vacuum from becoming too
great and causing damage to the bellows.

These are rather basic answers, so please ask for clarification
were needed.

Todd Augsburger - Roller Organs
http://www.rollerorgans.com