Owner's draws are not a business expense. They do not affect income. They will affect cash flows, but not income. Generally, a business owner pays tax on the income of the business regardless of the amount of draws.
No! An owner draw is removing equity from your business. It is not something you can count as an expense and deduct for tax purposes. It's simply taking money you invested in your business back out of the business
Any owners draw would usually be considered a liability. This is done to balance out the cash transaction on the balance sheet. A common way for this to be reflected is through a note payable to the owner. Depending on the company structure, this may or may not have a payback period associated with it.