Hemispheric dichotomy of Mars and unstable spin axis Is the following explanation plausible? Can you spot any flaws?
Mars doesn't have a large moon to stabilise its axis of rotation. At some point early in its formation its axis might have been pointing at the Sun with one hemisphere continually heating up and evaporating all the volatiles which circulated to the other side and froze. The extra weight of the volatiles would have compressed the surface leading to a thinner crust. As more volatiles were deposited on the frozen hemisphere compression would have continually kept Mars spheroidal by pushing the elevation of the frozen side down to match the other side's elevation.
Eventually the axis drifted away from this position so that the frozen hemisphere began to receive sunlight again and melt into an ocean. Over time Mars lost its atmosphere to space at which point the ocean also began to evaporate into space so that it lost volume resulting in the hemispheric dichotomy of Mars that we see today. As Mars lost heat to space the remnant ocean froze again.

 A: This seems possible if you also require some eccentricity of the orbit. For example, comets with highly elliptical orbits spend only a small fraction of time near the Sun, so the volatile ice on their surface doesn't get depleted for millions of years.
For Mars in a highly elliptical orbit, most of the year there would be summer on the South pole (with the Sun mostly directly overhead), and winter on the North pole. So ice would accumulate in the northern hemisphere. For a small time each year, however, the seasons would switch - the Sun would shine on the accumulated ice for e.g. 1/10th of a year. During that "polar day", the Sun would be much more powerful (Mars would be closer to it), but it's easy to imagine that all the ice would not melt immediately.
A highly elliptical orbit is problematic, however, because there is not enough space for it in the Solar system. It would intersect Earth's or Jupiter's orbit, unless it got lucky with some resonance configuration.
You would also need a mechanism for "circularizing" the orbit later. It could be performed by gravitational interaction with Jupiter. There is a model of Solar system evolution that includes Jupiter's orbital radius being 1.5 AU at some point in time. This makes some gravitational perturbations possible.
