He wasn’t hired through Mab, Nameless is still Winter but probably arranged to meet Marcone in a social situation before signing on with him on his own initiative. Marcone is Chairman of the Chicago Historical and Art Society (in Dead Beat Marcone choose some choice art from Bony Tony’s find) we know this through Death Masks a rich man’s club. A wealthy lawyer would fit right in, we know from the Law Nameless collects artifacts in his office so that would likely be where Nameless would make his approach through Marcone’s hobby before establishing his chops with the Cancer Charity thing. Hell his plan may have been for Marcone to approach him after watching him for a couple of years, Marcone does not make major decisions without considering every angle, and recruiting a supernatural lawyer not through Monoc? At that point “John” would have become Mr Marcone, and warned as such. We know though that Marcone hired Nameless after Small Favour, he might have felt he had an Ace in the Hole with Namshiel and could finally take the risk. Gard would have had to be overruled on that hire.
Yes Cowl did engage the Sorceror who stole the litter, that and setting up Mavra in Chicago to lure Harry in were his contributions to Death Masks (he likely called in the favour gained in Grave Peril as Harry had been engaged to track down the puppies a couple of weeks earlier). As regards scent, what Mouse tracks appears to be more than just normal scent, so the capability of being able to mask that may be problematic.
As pointed out Dresden uses mundane means as well as magical (Vince Graver springs to mind) so fingerprints are the obvious reason, and I have dealt with burned Justin as Cowl by pointing out that 24 years have passed, plenty of time to heal and the same for future Harry. The gloves may also be a countermeasure against his ‘scent’ rubbing off on things he touches, or Ash’s ‘scent’ rubbing off on him.