This is the last write-up on the topic, and it's much simpler:
For hand-pulled noodles, you need:
Bread flour (wet gluten 29-30%, protein 11%-12%)
45% added water
1% alkaline solution
kansui powder or (Lye Water + Baking powder) or Peng or Baking Soda
Ingredients (Alkaline solutions)
kansui powder
55% sodium carbonate (Na2CO3),
35% potassium carbonate (K2CO3),
10% sodium biphosphate dodecahydrate (NaHPO3.12H2O)
Lye Water
potassium carbonate (K2CO3) 74.5% in 100ml
sodium biphosphate (NaHPO3) 3.4% in 100ml
Instant ash Peng
sodium carbonate (Na2CO3) 90%
Sodium chloride (NaCl) 1.15%
It is recommended to use bread flour because of its higher wet gluten content compared to normal white flour. You will also need a small amount of alkali. One recommendation is to use kansui powder, due to its ph of 11. If kansui isn't available, the next option would be baking powder and lye water. If either isn't available, the next option would be to use sodium carbonate 1% of total weight flour weight (e.g. if you use 100g of flour, use 1g of sodium carbonate). If you're using a lower gluten dough like all-purpose flour, then baking powder will do just fine. If you're using cake flour, use baking soda.
(Remember to add the kansui/baking soda/baking powder/sodium carbonate to the flour and mix it in before adding water.)
Sodium carbonate vs. potassium carbonate:
I've haven't had success with bread flour, plain flour or all-purpose flour with potassium carbonate. Even though it increases the ph of the dough, it still does not give the dough its stretchability.
Why use alkaline solution in the first place?!
Alkaline solution will increase the water absorption and gluten creation of the dough to enable it to be pulled sooner than normal by leaving the dough to rest at room temperature for 45 to 60 minutes. The downside of the alkaline solution is that it also breaks down gluten after the peak absorption is achieved. So on one side you have faster absorption but on the other side the dough will become more resilient to pulling if left too long.
For a non-alkaline solution, use this tutorial. It will cover all the basics that you will need to learn, and you WILL need to use all-purpose flour or plain flour. Noodle flour works best.
In conclusion:
Without sodium carbonate it's possible to have hand-pulled noodles with any flour. The downside is you will have to knead the dough for 45 minutes and leave to rest for 2 hours until you can start pulling your noodle strands.
Without sodium carbonate the noodles are harder to pull and I had most success with cutting each strand and going from there from the video.
Milk is added to bread for flavour, a tender crumb and well-coloured crust.
Dry milk is used because it easy to store and easy to use in bulk. Milk also contains an enzyme called glutathione which can weaken gluten and result in a poorer quality loaf - the drying process destroys this enzyme.
You can substitute regular milk in various proportions, but you may as well simply replace the 2 cups of water with it, which will give you a nice soft loaf. Opinion is divided whether you should scald the milk (by heating to 180°F/82°C according to How Baking Works, page 150) to destroy the glutathione, but in any case it's probably a good idea to warm it anyway, to help the rise.
Best Answer
It doesn't have definite temperature because you don't need it. The dough will work with any temperature water you use, anywhere between 0 and 40 C. The difference will be in the time needed for the dough to rise, and the amount needed kneading to get the same gluten strength. But as these parameters are not firm, but you proof until the dough is risen properly, and knead until it is kneaded properly, you don't have to start with a specific temperature.
You don't need it for the milk either. But if the recipe author wants to spend roughly the same time preparing the bread, they must have used this temperature to achieve similar rising times for dough left to rise at room temperature, or maybe yeast left to proof at room temperature as suse mentions in a comment. It is just an additional convenience which can be followed, but is optional. So there is no need to supply it for the water either.