As already said
1st problem isn't a problem - when you aren't on the gas and in gear, engine management can cut fuel (maybe no completely, but as cfg said, potentially outside the SG's range). Many modern cars do this
As for the second...
Sounds like your radio has a problem o.0
a) does it happen when the SG isn't plugged in?
b) if no, did you try using the SG from another car in the silverado?
c) even if it only happens while the SG is plugged in, something tells me it's not the SG and a preexisting electrical problem (the SG is just making it evident).