I'm not quite sure why your slide isn't locking back, but your right slide release isn't broken. The H&K P2000 and P2000sk is famous for that "rattling" right slide release lever. My 9mm P2000sk V2 is the same way. A lot of people, including me, find it quite annoying. Nonetheless, it does not affect performance or reliability. Unless you are left-handed, you can actually take the right lever off completely and use only the left lever. It works perfectly and you don't have the "rattle" to annoy you. I don't think H&K should make a $800 pistol rattle anywhere, but for whatever reason they designed the right slide release lever w/ some extra play in it. 99.9% of the P2000s out there are this way, so it's definitely normal. They are fantastic guns otherwise and worth the premium without a doubt. H&K makes good stuff!
As for your slide not locking back, I wouldn't have a clue what's causing it if it's not operator error. H&Ks are probably the most reliable pistols money can buy. The chances of getting a lemon are slim to none. Make sure your thumbs are not riding the slide release when you shoot. A lot of 1911 guys tend to do this with their "thumbs forward" grip. Hope that was helpful to you...good luck and enjoy your new pistol!