Is any of this plumbing work a code violation?
All plumbing should be inside walls in finished space or it should be installed in a way that protects the joints and protects from punctures.
Who cares?  I never heard of plumbing failing because of elbows.
If you wanted this you should have been watching him during it.  Or another option is to just write it into the contract so you can set expectation.  As it stands you do not know which extra connections were actually needed or not.


4-5.  Have local inspector come out to OK it.  Don't pay plumber until it passes inspection.  

And to answer your question 1, 4, and 5 sound like they are code violations but we don't understand enough to call these violations.   For instance I can run pex in a crawl space in Texas, I can run pex in a laundry room outside framing (still not good practice), and you can run plumbing in most places in exterior walls (not good practice and most inspectors would want to see a reasonable level of insulation).