How can I check if my performance is improving?

The simplest way to check if you are improving is by comparing your last result with your previous ones. If your score is higher, then you are learning to put your skills into practice better, but also to quickly react to random events. 
You can see your previous results in the Analytics section by choosing your previous simulations in the filter, but also by looking at the graph at the bottom of the character's "Prepare the meeting" page.