A:
Hi! Unfortunately, though it may be confusing, Surface RT is not running full version of Windows 8, it's running a sort of Windows Mobile version. So it's more like a big Windows Phone, not quite a laptop.
Considering that: Chromecast is only compatible with Android and iOS, meaning that you won't be able to control a Chromecast with your Surface. If you happen to also have an Android (Galaxy, Nexus, HTC, LG) or an iPhone, then it's very much ideal for you to purchase the Chromecast.
If you have any questions, @JerryZaz on twitter.