How can I send SMS from my PC using my iPhone?
It is possible if it is jailbroken. I don't know if it works on the 3G or 4G networks, but it works on Wi-Fi.
Go into Cydia and install a app called "Veency" (this app will allways be active)
Install TightVNC on the computer you want to use for this
Run the program on your computer. It should be called "TightVNC Viewer" (not the server)
On your iPhone go to
Settings/Wi-Fi/Current Connectionand note your IP addressType it the TightVNC viewer along with your chosen password.
Enjoy typing from your PC!
I'm unaware of any way to do that with the iPhone specifically. You may want to look into using Google Voice though - it doesn't have superb integrated on the iPhone (Google tried; Apple rejected their app), but it's easy to send/receive SMS on your computer using your google contacts, and the SMSs get forwarded to your iPhone, and replies on your iPhone get sent back through Google Voice so it's all still in the online interface. I believe you can also sync your iPhone's contacts list with your google account's, so it won't be as smooth as with Nokia, but should work.
I'm afraid but at the moment it is not possible to directly (i.e. without user interaction on the iPhone) send SMS with the iPhone (at least not that I know of any).
You could try out myPhoneDesktop ( http://www.myphonedesktop.com/ , I'm not affiliated with them, just a user) or something similar, but you still have to click on "Send" on your Phone...
Getting notifications about incoming SMS on your PC: There's nothing for the iPhone I know of, sorry.
About reading the contacts list from your iPhone, I would advise you to sync it (e.g via Google, Yahoo or directly with iTunes and your local list).