Dough – I recently tried to make sourdough with the starter, it didn’t rise. Why is there still a crumb

First, try proofing your yeast (mix 110°F water, a little sugar, and a little yeast in a small container; confirm that it foams). It may be that your yeast is (well) past its prime. That's the most likely reason I can think of that your dough didn't rise.

Second reason could be that while mixing, the dough got too hot—heat will kill yeast. Yeast dies somewhere around 130°F, but really you want to keep it much cooler than that. If its getting too hot, consider starting with colder ingredients (e.g., ignore the instruction to warm the milk).

Finally, I'd suggest using recipes that are by weight; flour is much easier to measure by weight. You may be using a different scooping technique than the recipe author.

Also—there is something weird about that recipe. It lists 3½ cups flour in the ingredients, but then only has you add 2½ cups in the steps. I suspect that is a mistake, and explains the batter-like consistency you got.

The difference between flour marketed as Bread Flour and flour marketed as All Purpose (at least in the US) is the type of wheat from which it is milled, and therefore the protein percentage in the flour, a p/l value close to 1 which gives proper plasticity to the dough, and a large enough falling number to allow long fermentations.

At least the US, all flour marketed as either All Purpose or Bread Flour should be suitable for bread making, although bread flour will permit greater gluten development due to the higher protein level.

The yeast or bacteria in a bread starter eat the starch (after it has been converted to sugar by enzymes present in the flour), which is the bulk of the grain, whether the wheat is winter or summer, hard or soft, red or white.

Also, the way the bag is labelled is as much a marketing issue as a technical issue. For example, in the US, King Arthur brand all purpose flour is nearly as "hard" (high in protein) as other common brand's (such as Gold Medal) bread flour.

Use either all purpose or bread flour, as you choose.