What is the large scale structure of Mars?
The process of planetary differentiation for the inner 'rocky' planets creates an atmosphere, crust, mantle, core.
How does this compare to the earth?
What would we predict from Mars position in the solar disc, about the relative proportions of these three?
Core may be still partly molten. Core is lighter in density, and likely has more sulfur than earth. It may also have more radioactive material, and therefore radioactive decay may be a more important heat source.
Magnetic field: at present no global or core related field, crustal remnant magnetization does exist.
What is the lithosphere, what is the role of pressure and temperature in defining it, and how deep is it on Mars?
On earth crust comes in two types. On Mars? We know that much of it is basaltic, and that there are the southern highlands and the northern lowlands. the average difference in elevation between them is several kilometers. The lowlands are thought to be denser material and thinner crust than the highlands.
The importance of size to planetary evolution.
Some argue also that Mars started out colder.
What does the Tharsis bulge indicate about inner Martian dynamics?
Facts about Tharsis bulge - "the big zit":
Eylsium rise is second major hot spot. It is not diametrically opposed to the Tharsis region.
The importance of partial melting, and the footprint of mantle material involved in producing the Tharsis bulge. Basalts form from around 20% partial melt. This means a mantle volume some 4 times that of the magmatic output is involved.
Convection pattern in the Martian mantle: Walter Kiefer's model for Martian convection.
Great interest in the Martian geothermal gradient at present. Why? Because, if there is as much martian permafrost as thought, then the gradient determines at what level liquid water will exist in the crust, and this has important implications for the geobiology. However, most studies 'assume' what the gradient magnitude is.
Mars is very asymmetric in many ways. What might have initiated the asymmetry?
Good overview of Mars volcanoes, with lots of pictures. Only downside is comes with advertisements.
NASA summary of Mars volcanology, some with flybys.