Help? A Couple of Weird Bugs in 10.8.

Hey everyone!

I'm using a 15" Retina Macbook Pro that I've had since July. It's my first Mac after using Windows for the better part of about 15 years. Understandably, I don't know how a lot of Mac OS X works. On Windows, I would have a sort of "gameplan" whenever a bug or problem occured, but with the Mac, I don't have any clue where to start with these kinds of things yet.

Anyway, there are two specific bugs, if that's what you want to call them, that I'm trying to deal with. They'll both small and very non-critical, but they are annoying nonetheless.

I've tried searching for support for some of these (even tried AppleCare directly), and all of the fixes work for about 2 session (turn on --> turn off) before they're back. Here are the two problems:

1) The desktop background resets to the default galaxy image every time I restart. No matter how many times I change the background image, whenever I shut down and start up again, it always boots to the galaxy image. All of the dock and icons are normal - just the image.

2) Whenever I try to delete something, Finder pops up with a box stating "Finder wants to make changes. Type your password to allow this." Now, my system does not have a password, but I still have to leave the box blank, click on it, and press enter.

Like I said, neither are really that "critical" or "harmful," but they are extremely frustrating. Do you guys have any ideas for what to do with either of them? Thanks a lot! :)