C# Class of client methods for interacting with web servers
It's probably fine for test code. There are a few things I noticed. None of these are necessarily a problem. They may never affect your tests. But they're not ideal either. 


You're not calling Dispose() on everything that you strictly should (eg, Streams).
You're always encoding your post parameters in ASCII, but reading the responses in UTF8. If you're sticking to basic English characters that'll be fine, but if you try other languages/character sets it may be problematic. 
the GetStatusCode() function is using the HEAD method. Not all endpoints will respond properly to the HEAD method, or is the same way that they would to GET or POST. 


If you're going to be doing a lot of this then you may want to look at the WebClient class. It's a little bit simpler to use, and may be sufficient for your needs.