Can you have an Ultegra crank arm on the one side and a 105 crank arm on the other side
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.