You've not answered the questions of how you are connecting to the internet, what Mac you have (year and model), and what version of OS X you have.
OK... lets tackle problem number 1, which is Limewire.
Apart from the fact that it is used for the purpose of pirating, it has been forced to shut down by law.
Go to >system preferences>accounts click on your account on the left and click login items tab.
If Limewire is in there, then highlight it and click the
- underneath.
Now, connect to the internet with your ethernet cable to be certain that you get connected.
Next, to get rid of this Limewire, I would use AppCleaner
Apple - Downloads - System/Disk Utilities - AppCleaner
After this, I would download OnyX for OS X 10.6.x
Apple - Downloads - System/Disk Utilities - OnyX or 10.5.x
OnyX 2.0.6 for Mac free Download and click the automation tab and run it.
Next up, for deleting any application that has an uninstaller such as Microsoft office, use that uninstaller, where as 99% of applications you just need to drag them to the trash.
The reason I want you to use AppCleaner to delete Limewire is that it will find any rubbish that it has left on your Mac and send it to the trash, and then all you have to do is empty the trash.
Personally if I were you, since you are obviously very new to Macs, and I suspect that you have made a bit of a mess of things, I would wipe the HD and reinstall OS X.
So, first up, you'd want to use time machine and back up your computer onto an external HD. This is something that you should be doing regularly.
CLEAN INSTALL:
Boot from your install disc by holding C or option on start up.
Choose language and click next.
Go to utilities in menu bar and click disk utilities.
Select the HD in the left column and click erase tab.
Make sure that it is formatted as mac os extended (journalled) and click erase disk.
this will take a few seconds, then exit utilities, and continue installation.
When you are finished the installation, you will be asked if you want to restore your system from time machine backups.
At this stage I wouldn't do this, as we don't want to bring back any of the trouble that you backed up.
Now, run software updater over and over again until no more updates are available.
What I would next is run OnyX again.
Next, I would drag the contents of the documents, music and photos folders from the time machine backups on your external HD to the corresponding folders on your internal HD.
Last but not least, I would check out the following:
Apple - Find Out How - Mac Basics
http://www.mac-forums.com/forums/switcher-hangout/208133-sage-advice-new-mac-switcher.html