To pay in the federal payroll taxes and tax withheld, you need an account with the federal electronic payment system (EFTPS). Here is a link where you can enroll EFTPS . Once you pay in the taxes due, you need to file a form 941 and 940 to report the wages and taxes. Here are links where you can complete the forms online and mail in: Form 941 Form 940
You pay the other half of the social security and Medicare tax when you submit your deposit through the EFTPS. That part does not get reported on the W-2 form or W-3. It is ok not to report any federal income tax withheld.
The second link you mention should be sufficient to file your state unemployment taxes. It should not cost you anything to get a federal ID number or to register to pay state unemployment taxes or federal payroll taxes.
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