Does an old growth forest ecosystem produce more oxygen than it consumes?
Does an old growth forest ecosystem fix more CO2 than it produces?


The intergovernmental panel on climate change summarizes some of the data on carbon flux here. For the amazon similar tropical rain forests, it says:


  Measurements in pristine, seasonal tropical rain forests in Amazonia indicate NEP of approximately 1.0 t C ha-1 yr-1 (Grace et al., 1995a,b) and approximately 2.0 and 5.9 t C ha-1 yr-1 for dense, moist rain forest (Fan et al., 1990; Malhi et al., 1998, 1999). 


NEP is net ecosystem production, which, as I understand it, is essentially the total amount of carbon fixed by the ecosystem. 

It seems the tropics, and the Amazon, in particular, are important global carbon sinks. This is also discussed in this more recent article in Nature. 

This isn't my field, but as far as I understand it, forests are not closed or steady state systems. They do play a role as a sink in the global carbon cycle. I would assume net carbon fixation must come with increased biomass, so I may have just avoided a key part of your question. All the same, I think the point is that, again, even the amazon rain forest is not at steady state.

As far as oxygen is concerned, the report and article don't address it. I suspect this is because there is no documented problem with global oxygen depletion.