I've tried RCA shorting plugs as well as non-shorting caps on the open inputs of one preamp I was having noise floor problems with. Note, you don't want to short open output connectors, only inputs. I noticed very little though some improvement. I made my shorting caps using old generic IC's as Audiobugged suggests (though I soldered the cable ends to ensure they indeed were shorted). This is an easy and free way to test for yourself.
I can't address your question related to balanced inputs.
I can't address your question related to balanced inputs.