Can you have an Ultegra crank arm on the one side and a 105 crank arm on the other side I have an Ultegra groupset, but I also have a 105 left crank that has a power meter. Can you mix these two? I don't care about the weight difference, only talking about a geometry point of view. My left shoe and right shoe's cleats are in exactly the same position, but my left side shoe (at the contact point of cleat and shoe) is against the crank arm?
Yes, 105 and Ultegra components are largely compatible but it depends on the exact model numbers. Its best to check Shimano's compatibility charts.

I myself have a 105 crank on the left and an Ultegra on the right as the bump in my left Ultegra power meter crank won't clear my chainstay. They're both Hollow Tech II which means they're compatible.