What are the required documents you need to have in order to get a brand new passport?

In the US all you need is an old passport

Yes you can be denied

Read the website of the country you are a citizen of that you wish to apply for your passport all the answers are on there

You need to prove citizenship. E.g. for US, US birth certificate (original or certified copy) or Certificate of Naturalization. You need to prove your identity - govt-issued photo ID, such as driver's license or state DMV issued identity card issued in lieu of driver's license. Your Social Security card.

Passports can be denied citizens if they are under the jurisdiction of the court (e.g. on parole or probation for criminal conviction), if they owe back child support, if they do not provide adequate, acceptable proofs of citizenship & identity. For a minor child, US & a number of other countries now require in-person signatures of BOTH parents giving permission for child to have a passport.

Note each country sets its own laws & standards. For your country's passport, see their official govt website for their passport issuing authority for complete details on requirements, fees, application forms, etc.

In the USA and if you are a US Citizen, I believe you need a state issued photo ID, certified copy of your birth certificate, and two photos of a suitable size that can be used on your passport. And then the filled out application and check for the fee.

Last time I did it, it took about 3-4 weeks.

The requirements depend on your unknown nationality.

I can get a passport by just presenting the national ID card of my country at the town hall. I don't even need to fill a form, the admin clerk will do this electronically.

In other countries without mandatory registration you might need to show proof that you are a citizen, might need to fill a form, present a birth certificate, and a biometric passport picture.