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Is it okay to publish your replies on WikiNews and elsewhere (such as my science blog or wiki)?
Yes.

The temperatures for the highest levels of oxygen are really low -133 C, so, is the idea that this oxygen would be retained when the brines warm up to more habitable temperatures during the day or seasonally? Or would the oxygen be lost as it warms up? Or - is the idea that it has to be some exotic biochemistry that works only at ultra low temperatures like Dirk Schulze-Makuch's life based on hydrogen peroxide and perchlorates internal to the cells as antifreeze?
The options are both: first, cool oxygen-rich environments do not need to be habitats. They could be reservoirs packed with a necessary nutrient that can be accessed from a deeper and warmer region. Second, the major reason for limiting life at low temperature is ice nucleation, which would not occur in the type of brines that we study.

How quickly would the oxygen get into the brines - did you investigate the timescale?
No, we did not yet study the dynamics. We first needed to show that the potential is there. We are now studying the timescales and processes.

Could the brines that Nilton Renno and his teams simulated forming on salt / ice interfaces within minutes in Mars simulation conditions get oxygenated in the process of formation? If not, how long would it take for them to get oxygenated to levels sufficient for aerobic microbes? For instance could the Phoenix leg droplets have taken up enough oxygen for aerobic respiration by microbes?
Just like the answer above. Dynamics is still to be explored. (But this is a really good question 😉).

I notice from your figure 4 that there is enough oxygen for sponges only at tilts of about 45 degrees or less. Do you have any thoughts about how sponges could survive periods of time in the distant past when the Mars axial tilt exceeds 45 degrees, for instance, might there be subsurface oxygen rich oases in caves that recolonize the surface? Also what is the exact figure for the tilt at which oxygen levels sufficient for sponges become possible? (It looks like about 45 degrees from the figure but the paper doesn't seem to give a figure for this).
45 deg is approx. the correct degree. We were also tempted to speculate about this temporal driver but realized that we still know so little about the potential for life on Mars/principles of life that anything related to this question would be pure speculation, unfortunately.

And I'd also like to know about your experiment you want to send to Mars to help with the search for these oxygenated brines
We are now developing at “NASA/JPL-California Institute of Technology” a small tool, called TH2OR (Transmissive H2O Reconnaissance) that might one day fly with a yet-to-be-determined mission. It will use low frequency sounding techniques, capable of detecting groundwater at depths down to ideally a few km under the Martian surface, thanks to the high electric conductivity of only slightly salty water and Faraday’s law of induction. Most likely, such a small and affordable instrument could be placed stationary on the planet’s surface or be carried passively or actively on mobile surface assets; TH2OR might be also used in combination with existing orbiting assets to increase its sounding depth. Next to determining the depth of groundwater, we should also be able to estimate its salinity and indirectly its potential chemistry, which is critical information for astrobiology and ISRU (in situ resource utilization).

and about whether there are any future plans for using a more detailed model with time variation dirunally or seasonally.
Yes, we are now exploring the kinetics part and want to see what happens on shorter timescales.

Does your TH2OR use TDEM like the Mars 94 mission - and will it use natural ULF sources such as solar wind, diurnal variations in ionosphere heating and lightning?
The physical principle it uses is the same and this has been used for groundwater detection on the Earth for many decades; it’s Faraday’s law of induction in media that are electrically conducting (as slightly saline water is).

However, we will focus on creating our own signal as we do not know whether the EM fields needed for such measurements exist on Mars. However, we will also account for the possibility of already existing fields.

Does your paper's value of up to , 0.2 moles of oxygen per cubic meter, the same as Earth's sea water mean that there could potentially be life on Mars as active as our sea worms or even fish?
Mars is such a different place than the Earth and we still need to do so much more work before we can even start to speculate.

Some news stories coupled your research with the subglacial lakes announcement earlier this year. Could the oxygen get through ice into layers of brines such as the possible subglacial lakes at a depth of 1.5 km?
There are other ways to create oxygen. Radiolysis of water molecules into hydrogen and oxygen can liberate oxygen in the deep and that O2 could be dissolved in deep groundwater. The radiolytic power for this would come from radionuclides naturally contained in rocks, something we observe in diverse regions on Earth.

Could it get into a layer of fresh water just 30 cms below clear ice melted by the solid state greenhouse effect, as in Mohmann's model (which forms subsurface liquid water at surface temperatures as low as -56 °C).
See response above.

I know that the story is no longer "in the news" but it wasn't covered in great detail and I think there may well be a fair bit of interest in an expanded article about it. It does rather strkingly extend the potential habitability of Mars.
Our work really opens up new possibilities for the Martian habitability, and that’s why it’s so exciting!

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