In regard to the three problems mentioned:

1.  The split wooden connecting rod should clamp over the crankshaft
by the tightening of a single wood screw.  Are the screw's threads
stripped?  If so, the best solution would be to clean the oil from the
screw hole, with a solvent if necessary, and glue in a wood plug which
can hold the threads.  If the connecting rod is itself damaged so that
it will not surround the crankshaft properly, it can be replaced.  Use
the old one as a template.  (Drill the hole for the crankshaft, then
saw the split.)

2.  My _guess_ is that the exhale sound occurs because the leather flap
valve is too tight.  Is the flap valve held by tacks?  Just loosen it
a bit.  Hot hide glued?  See if heat will loosen the glue.  Or, can the
leather be stretched a bit?

3a.  If the driving arm on the shaft slips, I assume you mean that the
steel arm is slipping on the brass hub?  The first trick will be to find
the correct alignment for the arm.  As the shaft turns and the release
lever resets the mechanism to the beginning and after approximately one
or two more crank turns (where the song should begin to play), the
drive arm should be exactly _opposite_ the tips of the valve levers.
This of course assumes all the mechanism is in proper alignment and
that the trip pin is straight.  Another way to confirm the alignment
would be to compare the arm to the groove of the shaft.  Looking at the
shaft from the end where the arm is located, the arm will be about 165
degrees counter-clockwise from the groove in the shaft.

3b.  Once the correct location is determined, the arm can be set in
place by deforming the brass hub using a center punch.  However, you'll
have to be _certain_ to support the back of the hub against a solid
object, since the shaft is a soft material and easily bent, and the
cast iron supports are easily broken.  If you're not comfortable doing
this, then _don't_!  This is where a shop with proper tools might be
necessary.

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