Ross,  The particular "Concert" roller organ you have is, as you know
by now, one of the earlier models which has four exhauster bellows,
arranged like two double-acting.  Once you get it restored you'll find
the large air capacity gives it a superior sound -- you'll enjoy it!

Fortunately, from your excellent pictures it looks like the mechanism
is intact and complete.  When you order supplies like bellows cloth and
leather, be sure to get enough for this "rarer" machine; it requires
more than the later Concerts.  You can also get a set of felt/leather
valve pads (and hide glue too, although Player-Care.com has quality
glue as well) from

  http://www.rollerorgans.com/store/product_info.php?products_id=669

The broken linkage will not be difficult to make, especially since you
have the old piece as a template.  Cut a piece of wood to the proper
outside dimensions, drill the hole for the shaft, and then saw down the
center to allow it to "flex" over the shaft for installation.  Drill a
couple of holes for the screws, and you're done.

Speaking of screws: most hardware stores will carry enough variety to
replace the screws you're missing; there's nothing unusual here.  In
your pictures I did not see any hinges missing; the center panel is
rigidly mounted, and the front and back lids are each mounted with two
fancy hinges (which, believe it or not, are still a stock design at
many hardware stores).

Yes, fix the bellows and flap valves and get the mechanism into working
order.  It easily lifts out of the case, so you'll be able to play it
even before the case work is done.  I'm no expert on veneer so hopefully
someone else will advise you on that.

Look closely at the reed block: there's usually an ink-stamped or hand
written manufacturing date there.  Additional questions are welcome.

Todd Augsburger - Roller Organs
www.rollerorgans.com