To answer some of your questions...
What specifically is required for the Raspberry Pi to be used?
What are the strengths of the Raspberry Pi, including web browsing etc…?
The RPi is really poor at web browsing.
How can we get programs that are not on the pi on the pi? (We could get the source code for some of them)
There is a lot of software ready to install. See http://elinux.org/RPi_Install_software
What type of power supply is required (I know the rating, but where can I get one that works with the pi)?
Use any micro-USB power supply for a modern mobile phone or Kindle.