"Now that you have placed your hand on ..."
"Having placed your hand on..." is simply another way of saying this.
It may be easier to understand the sentence if you begin it with "Having placed..." followed by "would you be willing..."
So you mean I can change the sentence like that:
"Now that you have placed your hand on the Good Book and taken an oath before Almighty God Himself,Would you be willing to swear before a judge and jury?" But in fact he hasn't yet placed his hand on the Good Book or taken an oath,so it's just an assumption. "Assuming that you have placed your hand on ...,Would you be willing ...",So in this case should we use "will "instead of "would" here,Cus it doesnt seem to me like a subjunctive mood.