That’s a great observation. Let me do my best to explain.
1) The demonstration of the down block in the down block lesson and in the white belt kata, Basic 1, is what we would like to see. This is how you should demonstrate the down block throughout your kata(s) and one steps, etc. In the training guide, Sensei Jon uses a slightly different preparation for the down block. There are lots of little variations in how to prepare for a down block.
2) For practicing your kicks, both of these options can be considered correct. Practicing kicks with your arms down, next to the body, is a way to isolate your focus on the kicking leg and the core. It also helps you to maintain your balance, in the beginning stages of your training. Otherwise, you need to get into a good habit of bringing your hands up after/during a kick. When it comes to sparring and fighting, you don’t want to be caught with your hands down during or at the end of a kick, you will get knocked out. The arms down to the side is just an option for increased balance.
I hope that is helpful! -Sensei Michael