Strange behaviors on MacBook Pro before & after installing SL & new battery

Question

I have also posted this question in the Snow Leopard forum as I am not sure where it belongs. We have a MacBook Pro that up until recently had been running Tiger. A problem developed whereby we could not access the iTunes store. A message that the store was "not available at this time" came up repeatedly while at the same time another computer was able to make connections with it. In addition, when Firefox was opened, a prompt appeared to drag the Firefox icon to the applications folder. Even after this was done, the same prompt would appear during subsequent sessions.
We updated the OS to Snow Leopard, and the iTunes store problem was resolved. However, there are some other unusual things going on with other applications.
1. When Photobooth is opened, we get this message: "There is no connected camera."
2. When we open any of the Office applications, we are greeted with: "To open Microsoft Word (or Excel, PowerPoint, etc.), you need to install Rosetta."
3. The above-described issue with Firefox still occurs frequently. Even though Firefox is located in the Applications folder, there is now a volume named Firefox on the desktop. We can't get rid of it.
We don't know for sure if the Photobooth and Office issues were present right before the Snow Leopard installation, but they had worked properly in the past.
One thing we did do is a verify and repair of permissions. There were MANY that needed to be repaired.
In addition, right around the time SL was installed, the computer was frequently shutting off without warning. The mouse was also operating erratically. It was found that the battery needed to be replaced, as the existing one was expanding and was actually disrupting the operation of the mouse pad. Could this battery have been the source of these problems?
What are the next steps we should take?

Answer 1

I can deal with parts of this.
2. When we open any of the Office applications, we are greeted with: "To open Microsoft Word (or Excel, PowerPoint, etc.), you need to install Rosetta."
Snow Leo is very aware of apps that are not coded for Intel processors. This message suggests you have Office 2004 or older. Intel coding did not come to Office Mac until version 2008. Rosetta is an Apple emulation technology that lets apps coded for older PowerPC processors work on Macs with Intel processors. Most emulators do not give the performance of a program running natively.
You can either upgrade Office to the previous version 2008, buy a current Office 2011, or deal with the vagaries of emulation. Many people reported that Office 2004 had problems, particularly with keyboard input, when used on an Intel Mac.
NOTE: If you rely on Entourage for a mail client, Office 2011 has dropped Entourage. The business version comes with a new version of Outlook for Mac that replaces Entourage but the Home/student edition does not. If you go for Office 2011 and want to stay with mail features similar to Entourage, you'll have to get the higher-priced version.
One thing we did do is a verify and repair of permissions. There were MANY that needed to be repaired.
I would do it again because some of the things you describe sound like permissions issues. Sometimes, updates can install something that changes permissions. You should be using the version of Disk Utility on your hard drive, not the install disk, to insure the settings in your user folder are properly repaired.