this is nightmares http://www.cardgamedb.com/forums/uploads/1281656500/med_gallery_6_337535.jpg

let's say they have a maester with a bunch of chains. obviously what I want to do is blank their maester to discard all his stuff when he loses the maester keyword. are traits part of the text box?

Yes. Nightmares is common anti-maester tech, although it won't suffice if the Maester has an Apprentice Collar (they usually do).

this is old nan: http://www.cardgamedb.com/forums/uploads/1281901798/med_gallery_17_192384.jpg

what about old nan? lets say they have a maester with the apprentice maester attachment, and I use old nan so they lose the maester trait. their maester have the maester trait twice, does old nan removes both maester traits or only one?

As with pretty much everything "gains"/"loses" in this game, you add them up and apply the result.

1 Maester (printed) + 1 Maester (Apprentice Collar) - 1 Maester (Old Nan) = 1 Maester.