Welcome to the boards.
There are many free applications available through 3rd party application web sites (can be found in the Aftermarket Software forum) in addition to BlackBerry App World. Just from browsing around on this site, you will find many application threads with loads of information regarding great apps (both free and paid) that are available.
To answer your other question, you can upgrade either wirelessly or through your device. However, if you choose to conduct the "Wireless Upgrade" through your device (I have an option for "Wireless Upgrade" under the Advanced Options menu) then I believe it will only refer to your carrier to see if they have upgraded the software for your specific model. However, there are many versions of software released by various companies that can be used on any BlackBerry on any carrier, and in that case then you would need to install the software via connection to a computer. Because I do not have a MAC, I am not completely sure about how they function with BB's. As long as you download Desktop Manager and follow the instructions given in each "Latest OS
xxxx" thread specific to your device then you should be good to go. If you run into any issues, than just post up a blurb in the forum specific from your device and you're more likely than not to receive help within a short period of time.
Hope this helps.
Aftermarket Software forum: http://www.blackberryforums.com/aftermarket-software/