Mark, as usual has given the responses you asked about. I just have some questions/feedback to add:
First question is; Are the factors all continuous?
1. Yes, you left terms out of the model, hence the lack of fit dialogue. You could write a saturated model for the 44 degrees of freedom, but that would include cubic and quartic terms (and their interactions) for the 5-level factor and other non-linear interaction terms.
2. Full factorial are full resolution designs...therefore every degree of freedom can be estimated. Whether every term makes sense or not is a different question.
3. I'm not sure, but my guess is the non-linear interaction terms are not considered to be included in the model. I notice that when you use JMP to construct model effects and use the Response Surface Macro, the non-linear interaction terms are pooled in the MSE.
4. Doesn't matter what you call it, you can certainly estimate the quadratic effects for a factorial with factors at 3-levels.
"All models are wrong, some are useful" G.E.P. Box