Well first off, windows has a program built in to remotly contol a pc. You can do everything you mentioned and more.
First off, I have only done this with two computers which both have xp pro. I do not know what other OS's it works with.
Get to system properties, either by control panel or right clicking my computer and selecting properties. Navigate to the remote tab. check "allow users to connect remotely to this computer". Next go to another computer that is connected to the internet (dont forget to connect the computer you will be controling to the internet). Go tothe start menu>programs>accessories>communications>remote desktop connection. When you ge to the Remote Desktop Connection window, type in the IP address of the computer you want to control where it says "Computer:"
How many people can read hex if only you and dead people can read hex?
Start using reputation points!!!