I think there has just been so many posts about these types of glitches people just can't bring themselves to type you an answer any more

this is pretty well documented in the forums, but for the house issues specifically, moving forward for future houses you buy your best bet is:
- create a save point
- talk to the steward of the jarl who you want to buy the house from
- buy the house, and all of it's upgrades all at once, (so obviously make sure you have enough gold to do so). don't go to the house in between buying it and the upgrades
- once all is purchased, go to the house and test all bookshelves, weapons racks and plaques, mannequins, etc..
- if any are glitchy, reload your save and start again with the purchase.. if everything seems to work.. continue playing.
I've just made this routine my standard operating procedure now whenver buying a house, and it seems to keep me from having glitches..
one other note.. if you have any intention of buy the house in windhelm, Hjerim, go to windhelm early in your game and make sure the Blood on the Ice quest triggers and works correctly. you'll want to search for that one, but again, it's very well documented the issues with that quest. if it does not work however, you will never be able to buy that house.