For the W-9, you may use your EIN. Since this is given to private, non-secure sources, I would highly recommend using the company EIN rather than your Social Security Number. Additionally, your business is in dealings with the payer, not you personally.
Estimated Taxes paid are reported on your personal Form 1040, not on schedule C. The estimates go towards your personal tax liability, not just your tax liability based on your business income. For all these reasons, your estimated tax payments should be paid attributed to your personal social security number.
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