Do I need to pay quarterly 1040 ES and 941 (payroll)?
I'm not sure why you're confusing the two unrelated things. 1040ES is your estimated tax payments. 941 is your corporation's payroll tax report. They have nothing to do with each other. You being the corporation's employee is accidental, and can only help you to avoid 1040ES and use the W2 withholding instead - like any other employee. From the IRS standpoint you're not running a LLC - you're running a corporation, and you're that corporation's employee. While technically you're self-employed, from tax perspective - you're not (to the extent of your corporate salary, at least).