Congratulations, I will be picking up my L&H Buescher stencil from my tech tomorrow, following a complete refit. Speaking to him yesterday he said the horn, using a tenor mouthpiece, now sounds like Coleman Hawkins without the edge; I look forward to not sounding like a 4 yr old on a kazoo.
As to your questionsn I hope the following will help-
To get rid of the green spots try WD40, if that doesn't work apply ammonia, use a cotton bud and avoid pads, corks etc, and wash off with water. Failing all the above a minl tool (eg dremel) with a brass brush will do the job, done carefully this should not damage any intact plate. Any bare areas can be touched up with silver plating formula, although these will not be satin.
I am surprised that alto reeds fit as these are much to narrow for my mouthpieces, you may want to try tenor or bass clarinet reeds. There are several new c melody mouthpieces now available some of which are getting good write ups. In addition many c owners use tenor mouthpieces which seem to give good sound and intonation.
I recently read a claim that the serial numbers on Buescher stencils follow the main Buescher list, so looking up any of the available lists may give you a good idea as to age.
For a wealth of info on C's, including serial lists, try www.cmelodysax.co.uk.
Hope this is of help.
Paul