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You will need to have your corporation
formed before it can enter into a contractual relationship. If you want to get the consulting engagement done before you form your corporation, what you would want to do is enter into the agreement personally and have a provision in the agreement that you have the right to assign it to your corporation upon its formation at which time all rights, duties and obligations are assumed by your corporation and the other party agrees that you are released personally.
With regard to your second question, the reason to form a corporation is for the limited liability aspect...where your personal assets are protected from the debts and liabilities of your corporation. To make sure you maintain that limited liability, you want to treat the corporation as a separate and distinct entity and not co-mingle things between your corporation and your personal accounts. Thus, you don't want to use your personal bank account for your corporation's business
; rather the corporation needs its own accounts to avoid a creditor later being able to "pierce the corporate veil" and pursue you personally for corporate debts and liabilities.
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