2 questions

first, how do I hide the mouse curser? And second, how do I alpha blend so that the black parts of the texture are completely transparent?

// hide the cursor
ShowCursor(false);

If you want to blend You should first look at some tutorials in http://nehe.gamedev.net

// To blend We’re using:

glEnable(GL_BLEND);
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);

// draw the primitives

glDisable(GL_BLEND);

cheers,
yaro