What drawing methods can I use in the Win 8 Phone SDK to manually draw single pixels on the screen, like in a drawing app?
It doesn't matter if its c#, c++ or something else.
Use WritableBitmap.Pixels collection to manipulate pixels directly and display them on the screen by setting Image.SetSource(myWriteableBItmap).
Since WriteableBitmap is a bit sparse, you should pick up WriteableBitmapEx that adds lots of 2D rendering functions to WriteableBitmap. See more at @ http://writeablebitmapex.codeplex.com
For on-screen drawing you should consider using InkPresenter as it's much more suited to handle those usecases @ http://www.nickharris.net/2010/03/silverlight-for-mobile-on-windows-phone-7-inkpresenter-fun/