Question: I have to buy a Raspberry Pi to control a monitor remotely. 

1. Can I install software like [TeamViewer](http://en.wikipedia.org/wiki/TeamViewer) on Raspberry Pi?
2. Can I connect the Raspberry Pi via wireless or LAN?
3. Can I connect an Internet key to a Raspberry Pi?

Answer: 
TeamViewer cannot be used on the Raspberry Pi at this time. They do not have a build for it.

You can install a [VNC](http://en.wikipedia.org/wiki/Virtual_Network_Computing) server, and that would be your simplest option. You would have no issues connecting on your LAN, however if you wanted to connect remotely, you would need to set up port forwarding.

An alternative to port forwarding would be to use a NeoRouter or Logmein Hamachi, both of which can be installed on the Raspberry Pi. (The software would also need to be installed on the machine that you are using to connect to it.)
<http://eltechs.com/run-teamviewer-on-raspberry-pi/>

Try with ExaGear!

"TeamViewer is pretty popular remote access software but unfortunately it is not available for ARM-based devices such as Raspberry Pi 2. Fortunately there is a way to run TeamViewer on Raspberry Pi 2 using ExaGear Desktop which allows to run x86 apps on Raspberry Pi 2."