If kindly man is killed, can you use the new aryas ability or does his state change to moribund: agenda negate the opportunity?

I could be wrong, and I am sure someone will correct me if I am. But i would say yes you can use her ability if the kindly man is killed before he becomes an agenda

Indeed, The Kindly Man was killed, regardless of his final destination.

Another question, if you trigger TKM's ability to take an opponents character from their dead/discard pile, is that considered changing control for something like the bastard of bolton (because the kindly man says put into play under your control)?

I would think not, since a card in an opponent's dead or discard pile is not under their control at the time you take control of the character (so it's not changing control). HOWEVER, if I'm wrong, please let me know so that I can put Bastard of Bolton into my Kindly Man deck!! =)

Bringing something into play from an opponent's out-of-play area is technically a control change. It starts in one person's control (yes, you do "control" the cards you own that are not in play - they just are not normally actionable) and ends in another's. If it wasn't a control change, it would revert to the default "owner's control" immediately upon entering play.

The question is whether or not it is an actionable control change. It probably is (and I half remember a ruling to that effect related to some CCG version of Balon). So, Kindly Man should be considered a "take control" effect when used on an opponent's character, which would allow you to Respond to the control change with something like the Bastard of Bolton.

Note that this doesn't work in reverse (ie, it is not an actionable control change when A takes control of B's card, then control goes back to B when the card leaves play) because the control change doesn't take place until the card is physically removed from play - after the chance to Respond has passed.