1) The law would be made ineffective if it wasn't appeased; the Witch claimed Edmund by right of the law and the Deep Magic, so if Aslan just announced that it was overruled, the law and the Deep Magic would be completely out the window. I don't know what (if any) physical effects there would've been, though? Maybe the Witch wouldn't have been accountable against any law, though?

2) Aslan knew he wouldn't be there to lead the battle and as Peter would be High King, putting him in charge of the battle was a good way to show that and to have him start acting like king, kind of.

3) The White Witch hated Aslan and shaving his mane was a way to rub it in his face that she had "beaten" him.

4) Maybe because he was still quiet and longsuffering?

What do you think would happen if the Deep Magic were not appeased? Why couldn't Aslan just announce that he overruled it?
Just what the witch said would happen. Narnia would perish in fire and water. It was the Emperor's magic not Aslan's. Even if it were his magic, he would not overrule it. He follows his own rules.
Why did Aslan make Peter in charge of leading the battle?
Peter was going to be High King so he is the most logic person other than Aslan.
The White Witch ordered her troops to humiliate Aslan by shaving his mane before she killed him. Why do you think she did this?
She hated him and wanted to make him suffer.
Why do you think Aslan looked braver and more beautiful to Lucy after he had been shaved?
Maybe His mane was in his face before? I think it was influenced by what he was allowing to be done to him.
What stood out to you about this chapter? What did you like? What didn't you like?
I like that Lewis writes, " and other creatures whom I won't describe because if I did the grown-ups would probably not let you read this book."

What do you think would happen if the Deep Magic were not appeased? Why couldn't Aslan just announce that he overruled it?
I agree with what's already been said--it's the Emperor's magic, not Aslan's, and the consequences would've been devastating for Narnia if he'd just ignored it. Besides that, Aslan is unwilling to disobey the law--as we discussed last chapter, he doesn't even consider it a viable option.

Why did Aslan make Peter in charge of leading the battle?
Like Valia said--Aslan knew he wouldn't be there, and the soon-to-be High King needs to know how to lead an army.

The White Witch ordered her troops to humiliate Aslan by shaving his mane before she killed him. Why do you think she did this?
Perhaps just to assure herself that Aslan really was surrendering himself. Besides that, this is her one opportunity to demonstrate complete control over Aslan himself--why would she waste it?

Why do you think Aslan looked braver and more beautiful to Lucy after he had been shaved?
I think because, at that point, she could see all his nobility, like Valia touched on. Perhaps she had already realized why Aslan was doing this, and now that she knew that Aslan was enduring all this torture for her brother, her love for him was deeper than ever before.

What do you think would happen if the Deep Magic were not appeased? Why couldn't Aslan just announce that he overruled it?

Work against the Emperor's Magic?!?!?!?!

If the deep magic were not appeased, all of Narnia would be overturned and perish in fire and water.

Aslan couldn't and wouldn't overrule the deep magic. That would be treason.

Why did Aslan make Peter in charge of leading the battle?

In a practical sense, it does seem a bit strange, -letting a boy lead an army. I think it has a lot to do with destiny. Peter was supposed to become king and he already had the qualities, he just didn't have the experience. Peter proved himself in one-on-one combat. The next stage was to wage a battle. But don't worry, I'm sure he had advisers.

The White Witch ordered her troops to humiliate Aslan by shaving his mane before she killed him. Why do you think she did this?

Spite.

Why do you think Aslan looked braver and more beautiful to Lucy after he had been shaved?

It probably wasn't necessarily his appearance, but rather his actions. He chose to lay down and bear it for Edmund's sake rather than retain his dignity and sacrifice Ed.