Can I run Selenium on Computer A, and see the browser in Computer B?

Question

Imagine I have some Selenium Project ready on Computer A. When you run this project, a new browser opens in Computer A, and connects to www.somesite.com and runs the tests..

Answer 1

That's exactly what Selenium Grid is for!

Have fun

And please reconsider the usage of Selenium RC which is actually an undead, better use the RemoteWebDriver instead.