Yes, both state and federal just like anyone else.
They also pay Social Security tax (except for certain employees that began their careers before 1984). All members of Congress pay Social Security tax.
Yes. In the United States, the Federal Government pay levy taxes on income. As the initial proposition for what became Amendment XVI had no time limit, and since more than 3/4 of the states have...
Your taxes must be paid through out the year. That is, by either payroll withholding or making estimated payments on your estimated amount due quarterly...with a Form 1040-ES.
Not making payments...
Yes, However, you are tax free only on a portion of it. The amount you (personally not jointly with the government) put in, is deducted on a percentage basis. You need to contact IRS (or go to there...