I have an 80+ year old English Tudor with a half beam and stucco exterior. Unfortunately some of the beam are terribly rotted and I am not sure what to do about it. I believe the wood to be cedar and in addition to the decay, gaps have developed between the beams and the stucco in many places. There are also some areas where the stucco needs to be repaired/replaced. Lastly, the exterior needs to be repainted.

I live in the Western Suburbs of Chicago and have had very poor luck with contractors in general. It usually seems that rather than hiring craftsmen, I am simply hiring day laborers and it shows in the results.

My questions are:
Are there any suggestions about how to fix the rotting wood issue?
What type of contractor would I use for this work?
Where can I find a stucco contractor (I have looked without success)?
Should I caulk between the wood and stucco to fill the gaps (if not, what should I do)?
I have heard that stucco should not be traditionally painted, but needs to breath... Is this true and if so, what is the procedure for painting the stucco?
The exterior wood needs to be stripped and either painted or stained... Any thoughts on painting vs. staining?
Any suggestions for specific contractors in the Western (or greater) Chicago area who can do some or all of this work (or rather who can do this work competently)?

I am quite good at home repairs and remodeling, but for something like this I am more comfortable having a knowledgable professional handle the job.

Thanks.