No, businesses directly pay the federal government. More insidiously, it's impossible to opt out if you're employed full time; you have to be self employed to get to decide when/if/how much tax you send the federal government.
Apparently before 1943, people paid taxes individually once a year. Then a law was passed requiring their employers to do it regularly instead without their consent.
Maybe. But the biggest employers are national if not international. They're gonna withhold federal tax.