Out of curiosity: is "hij opent het raampje" correct? If so, what's the difference in nuance between the two?
That one is fine too. The difference is the verb that is used: 'opendoen' vs 'openen'. Both mean 'to open'.
Hij gaat het raampje open doen = he is going to open the window. Hij doet het raampje open = he is opening the window. Het raampje gaat open = the window is opening/the window is designed to open.
I know you asked this question a long time ago, but maybe someone still needs the anwer.
I have yet to see a sentence with "gaat open", but I'd guess it is about the source of the opening action. Thus, "hij doet het raampje open" has a distinct source ("hij") who is repsonsible for opening the window, while "het raampje gaat open" would mean "the window opens" or even that it is possible to open the window, as it is not locked or something.
There are some examples of "open gaan" in this list that support the idea: http://nl.bab.la/woordenboek/nederlands-engels/gaat-open