Since turning off my cable TV, i would like to view some of my TV shows from the various network websites. Can i use RPi to do this, so i don't have to invest in a larger PC or laptop for this minimal function?
Yes you can.
If you have a spare SD card or are happy to use your existing one you could install Raspbmc (as a dual boot).
There are plenty of guides to installing it and there is also Sam Nazarko's book available on the Raspbmc website.
I wrote an article last year on setting up Raspbmc which you may also find useful:
There are some links there for the plugins you will need to watch BBC iplayer, Amazon VoD etc. as well.
Yes. The Midori browser may be limited, but it's faster than the Chromium browser. Here are the instructions to get HTML 5 videos to play on either.
Get HTML5 videos to play in Chromium on Raspberry Pi