So your 'K11' would actually be either a 'G11' or 'G96/11', the way to tell between the two is the G96/11 will have a grafted pistol grip and a cupped buttplate instead of a flat buttplate. Many importers called 'G11s' and 'G96/11s', 'K11s' for whatever reason.
They are fairly straight forward rifles to take apart once you understand how to disassemble the bolt. Not really much to avoid for the most part, they are very well made guns with very well thought out designs. Only thing that really matters and is different on these rifles than most is using a good grease on the bolt, not oil.
The
Swiss
also took excellent care of them so they tend to be in pretty good condition if they are as they left Switzerland. There also can be a 'Troop Tag' under the buttplate as well, so I would take a look under there, on my Swiss rifles my K31 and K11 have one but the rest don't. Just a neat bit of personalized history.
I absolutely love these rifles, you made two great purchases from the sounds of it.