What windows api function does internet explorer use to display text in the browser window?
What functions does the WM_PAINT or WM_NPAINT event call in internet explorer to display any text?
For example if a google search returns some results, what windows api is being called to show the result in the browser window?
Well, the layout engine that powers IE is called Trident.
The rendering API used does depend on which version. I believe IE8+ uses DirectX 2D to do most of the rendering.
Previous versions would (I suppose, but not sure) use the standard GDI+ drawing functions for rendering.
Why don't you make a little application that uses the IE WebBrowser COM component, and then trace DLL calls made by the app?
Edit: Easiest way to do a tracer application (and I can't believe I'm saying this) is to make a little VB6 app, add the Internet Explorer control onto the form, and have a button that triggers a single page navigate (use a really simple page, preferably a local one that you've made yourself). Run that app as an exe (not in the IDE), and then attach a profiler to it like API monitor, or just google 'win32 api trace'.