Rathound suit, he gives even without kidnapping the gal - it suffices to just convince both him and camp Hathor to make a truce: get the quest to kill him, then go talk with him and convince him to propose a truce, then go back to Hathor and convience the boss there to accept the truce, then go back to King one more time and tell him Hathor agrees to the truce. Right after that, he gives the suit.
As for training, it really looks like the King would offer some sort of Traps skill training - there is a gialog line with him asking about traps in general, and another one specifically asking the King to teach player character. So you see, it's strange to me that 2nd line exists, if the only possible outcome for trying the latter, in 100% cases - is "no i won't teach you". It'd be enough to have just 1st line, then. Just feels weird, man. This is why i suspect it's either a bit of cut content, _or_ there is actually some way to actually have King teaching us something.
Perhaps some special feat, like "Hunter" which camp Hathor's boss teaches after truce is made - but perhaps the King's special feat only happens if we side with King and wipe out camp Hathor whole? This would be kinda logical, you know.