As I understand it 'most' court settings give you the option before hand to request a secular oath otherwise they default with the 'I swear to God' version. It appears dependant on State law and since the Senate committee is in DC...

Code of the District of Columbia

§ 14–101. Evidence under oath; affirmation in lieu of oath; perjury.
(a) All evidence shall be given under oath according to the forms of the common law.

A witness who has conscientious scruples against taking an oath, may, in lieu thereof, solemnly, sincerely, and truly declare and affirm. Where an application, statement, or declaration is required to be supported or verified by an oath, the affirmation is the equivalent of an oath.

Whoever swears, affirms, declares, or gives testimony in any form, where an oath is authorized by law, is lawfully sworn, and is guilty of perjury in a case where he would be guilty of that crime if sworn according to the forms of the common law.

[code.dccouncil.us]

Yes, but mostly done and believed by Republican men. These are the guys that still believe a court of law has people swear on the bible to "tell the truth" just like in an old 1940 movie. They play this drama out in real life today with hope that everyone will believe it.

A polygraph is not conclusive of anything. I once had to take one for a job position. To warm up for the real questions they asked me to "tell some lies" while they watched the machines reaction. It's like adjusting a control until you get the result you want and mostly it measures breathing and heart rate etc. during a series of questions.