Plotting a mineral stability diagram
Remember that you are concerned about stability fields. The lines on your stability diagram are the places where two minerals are in equilibrium. One one side one mineral will be more stable, on the other side the other one will be.

Let's talk about $\ce{Ca}$ first. The reactions all have the same $\ce{Ca}$ so it's activity isn't a factor in their relative stability. If you write a combined reaction for any mineral to another, it will cancel out. Try it. Calcite stability has nothing to do with $\ce{Mg}$ or $\ce{SO4}$ it's stability will only depend on $\ce{CO3}$ and $\ce{Ca}$. But wait, you know $\mathrm{ln}\,a_{\ce{CO3}}$ so you can calculate $\mathrm{ln}\,a_\ce{Ca}$ in equilibrium with calcite. So you can use that to help figure out where calcite is the most stable.

You only have one equation where sulfate is included. What direction will that stability boundary take on your diagram? Say you want to divide your diagram space into areas of calcite vs gypsum stability, how could you combine the two solubility equations to come up with the conversion of one mineral to the other? What dissolved species activities enter into the equation (hint: you know one of the two). Given that you can figure out the other one and plot that on you diagram.

Can you follow a similar process for calcite and dolomite (hint: yes)? What about calcite and huntite? Is there any part of the diagram where huntite is more stable than dolomite (or vice versa)?

Now figure out the stability relationship between dolomite and gypsum. What angle will the line take on your plot? Figure out where it will occur by combining reactions. This is a bit trickier but the $\mathrm{ln}\,a$ values will depend on the $\mathrm{ln}\,K$ for the combined reaction.

Now erase any lines in a field where those two minerals are less stable than anything else.

Good luck and let us know if you get stuck. I didn't want to just give you the answer because I'd have to actually work it out.