New Macbook Pro for Christmas = Questions!

Hey All!
This was a great Christmas! I got a new 15" Macbook Pro.... 2.33GHz Core2Duo, 2 gigs ram, 120gb HD.... it is a beauty and I couldn't be happier. This is my first Mac ever. I am a computer science major and have used nothing but PCs my whole life.
I have been reading up on OSX for a while and I am learning pretty fast. I have questions regarding installing applications and downloading:

1)I downloaded Adium using Firefox. I set Firefox to download everything to the desktop. After downloading Adium, there was nothing on my desktop besides my Macintosh HD icon. Upon searching for Adium using spotlight, its says the dmg file for Aium is in 'Documents.' My documents folder is empty, however. If I try to d/l Adium to the desktop again, it says it is already there. What am I doing wrong?

2) Another question I have is in regards to the trash. When I right click the trash and click 'Empty Trash', I hear the sound effects, hwever, upon opening the trash, the items that should have been emptied are still there. When I click on the items, only then do they diappear out of the trash. Any thoughts?

Thanks in advance for any insight you all might have on these subjects!!!

Both behaviors are quite contrary to normal OS X behavior. Is your system up to date? Check for software updates and make sure that you have all the latest and greatest. Somehow, Mac OS X is failing to auto update your desktop as things change, and your trash can as well. Most unusual, and it suggests a software issue - perhaps the Mac had been partially updated but not fully, or some such, just before "Santa" wrapped it up for you? I would recommend getting into a known, up to date state, and then trying again.

If all else fails, create a new userid for yourself and try that. Something may be messed up in the default user id.

BTW, since you are a new Mac user, I should point out that this kind of thing is MOST unusual for a Mac. One of the great things about them is that by and large, they just work. You don't have to mess with this sort of thing, like you do with Windows. Hopefully, this is the only issue of this sort you experience!

Thanks for the response mac. I made sure everything was updated (which it was) and I rebooted. The computer actually got stuck on the reboot and I had to hold down the power button to turn it off. Upon turning it back on, Everything seems to be as it should. Downloaded programs show up on the desktop and the trash empties by itself. Seems to be fine. Kinda strange but if it works now, I'm happy. I love this computer, it is so awesome! Ill let you know if anything else squirrelly happens. Thanks!