I make gingerbread houses every year. Walls should be approximately 1/4 inch thick. I have found that cutting the pieces first to work best. Yes there is some spread, but when they come out of the oven, I replace the stencil and trim up any spread (for the straight outside edges, a pizza cutter works well). I know it sounds redundant, but sometimes I don't cut quick enough, or I am distracted by the phone, or any other number of things, if I only cut after baking. With the items pre-cut, if I get distracted, I at least have a usable part. Granted I may have to shave any spread very gently with a microplane or the edge of a knife, but that is just what works for me.
I also will roll the dough out on parchment paper, cut and remove the excess, then slide the whole thing onto a pan for baking. This way, you don't get any "stretch" of your pieces. I have several square cookie cutters that I will use to cut out the windows and such. I make the windows rectangular by using the cookie cutter and cutting a square then moving it and cutting another half square. This is helpful because when the gingerbread comes out of the oven, you don't have to spend a lot of time with a knife trimming the inside of all the windows... you just punch any spread out with the cookie cutter.
As Sobachatina mentioned, melted sugar makes beautiful windows. I however, will lay the walls on a silicone mat and pour the sugar directly into the window holes. No need to "glue."
I'd hate for you to make a gingerbread house with the "wrong" icing. You want an icing that will dry rock hard, like cement. For this you will want to use "Royal Icing."
For larger houses, use canned goods to hold the walls in place while the icing dries. The house should be built at least one day before you start decorating, to be sure it has set up really good.
You didn't knead it enough in the first place. 2 minutes is too short even with the pasta machine afterwards.
Pasta, especially the classic semolina pasta (which is mae with durum semolina), is a high-gluten product. To make it correctly, you need to develop that gluten. I don't make semolina-water pasta, but knead my flour-egg pasta for around 8 minutes. It makes a great dough, and you can feel the change in texture while kneading. Of course, dough with that much Glenn is way too tight to work it. Very hard to roll, resists cutting. That's what you need resting for: to relax the gluten. Else, shaping becomes a heavy chore.
There is no food police which will come to arrest you if you make noodles with underdeveloped gluten, but most people prefer the slightly resilient texture of developed-gluten noodles. You describe yours as "having a great bite", and apparently they didn't fall apart in the boiling water. So you could make both side-by-side and decide which is more to your taste. I you stay with the ess kneading, you will need less to no rest.
Best Answer
In most wheat-based recipes, gluten strands are formed while you work the dough. If you don't rest the dough, rolling can be more difficult and you may get a tougher texture in the final product.
Additionally, refrigerating the dough up to a certain point will firm up the fats in the recipe (butter, etc), which will make the dough less mushy and will making rolling out the dough evenly a bit easier. Unless the dough is so firm it becomes brittle, refrigeration will make the dough less fragile in most cases.
Perhaps less important, the moisture levels may become a bit more consistent throughout the dough as well.