ANOVA output of RSM

Hi! I've implemented a Python app for response surface modelling (design of experiments) to better understand the topic. It works just fine - I can create design matrices, fit a polynomial model to the response and find the local minima/maxima of the model. I've been using it at work for a while (biotechnologist, btw) and it works in real life as well. The rest of my company found out and started using it as well. Now they all started coming to me as the "design of experiments expert".
I don't feel like one, I'm just a biologist that likes to code a bit, but I figured I better dig deeper into the topic and understand it as much as possible.
One thing that I'm still not quite sure about is the final ANOVA output most people show when they do this kind of modelling. From what I could gather (it's surprisingly difficult to find this info, most of it is just about what buttons to click in X software), you do:

1. an ANOVA comparing the SS residuals of the model vs the SS residuals of mean of the population
2. the same for each individual term of the model, to choose terms your model actually needs (though I rarely see people "prune" the general 2-nd order polynomial)
3. All commercial software also adds some SS measure for "residuals" - this is what confuses me. What residuals are looked at here? How would I calculate this manually or rather, what from?
4. And an anova for "lack of fit" - which also still confuses me. I have no idea how this metric would be calculated.

Maybe these things are so obvious nobody's ever thought to write them up, but I'd love an explanation!