To do the middle mouse button:
# Fn + Shift + Tap : Center click
I looked over the Xqt source code for how it handles choosing which button to choose but I don't have many answers.
At line 330 in qtscreen.cc you have this function
void qtScreen::mouseButtonEvent(QMouseEvent *ev, int isPress)
which interprets ev->button() to decide what mouse button you want.
I think ev->button() is passed from Qt because the case statement refers to LeftButton, MidButton, and RightButton which are also found in qnamespace.h. This says to me that the mouse button control isn't even a part of Xqt but comes from Qtopia. Maybe someone with with Qt development experience could enlighten us. This doesn't mean it still can't be remapped inside the X server, I don't know what applications to use though.
I checked out to see if xmodmap could be used to modify the mouse clicks, but I didn't come up with any usefull information. Have you checked out KeyHelper? I never tried running it, but maybe that can do what you are looking for.