I know in N3 this was stated to not be the case in the rulebook, and sorry if this has been asked before, but do troopers with a bonus to cc attack damage and a pistol apply it when using their pistols in CC?
Yes it affects all CC Attacks, unless it's the bonus from Martial Arts which only affects PH based damage.
Yes, on a similar note, if the pistol specifically has +1B it gains the extra B in close combat and shooting.