If you wish to estimate interactions, when you are specifying design you need to tell JMP that your model has interactions. You chose a Screening design. That coupled with the high number of levels for the categorical factors will prevent the estimation of interactions. Screening designs are not intended to estimate interactions in most cases. Screening designs are for identifying main effects.
Using your factors and response, I chose to make a Custom Design. I specified that I wanted a model with all main effects and all 2-way interactions. This will require a minimum of 262 runs (280 runs recommended), as Lou Valente noted. However, WHERE those 262 runs are placed is important. Screening designs may not place the runs in a spot that allows the estimation of the interactions (see above of the goal of a screening design).
I simulated response data for the 280 run design (the recommended number). I have attached that data table. When you analyze the data, you should see that your interaction plots are indeed active.
Dan Obermiller