Yes, your S Corp will have to file Form 940 and pay FUTA taxes for you (the employee) even if some other company is already paying for you.
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Please note: This advice is provided with the understanding that all the relevant facts have been provided by you. Any change in facts might affect the advice given and hence may not be relied on in such cases.
It is paid by the employer on the first $7000 of each employee's wages. Since you are working for two employer's (incl your S Corp) each employer will have to pay on the first $7000 paid to you as wages.
You cannot collect 2 employment checks but your compensation will be calculated based on your total earnings from the two jobs.