Is it normal for auditors to require all company passwords?

Is this normal for a pentest?

Absolutely not. Best case scenario: they are performing "social engineering" penetration testing and want to see if you can be pressured into fulfilling a very dangerous action. Middle-case scenario, they don't know how to do their job. Worst-case scenario they are only pretending to be an auditing company and fulfilling their request will result in an expensive breach.

In the case of a code-audit the company will obviously need access to source code. However I would expect a company who provides such services to already understand the sensitivity of such a need and have lots of forms for you to sign, and to offer to work in a strictly controlled environment. A reputable security company is going to be concerned not just with protecting you (because it is their job) but also with protecting themselves from untrustworthy clients (Our source code got leaked right after we hired you: we're suing!!!!). All this to say: any reputable security company that doesn't have you sign lots of contracts before going to work is not a reputable security company.

I can't imagine any circumstances in which handing over access to any of those things would be a good idea.

Edit RE: hidden contracts

A few have suggested that the company might have simply not told the OP about any relevant contracts/agreements/NDAs. I suppose this is possible, but I want to clarify that the lack of a contract isn't the only red flag that I see.

As someone who has built e-commerce sites and business software that has required integration with many CC Processors, I see absolutely no benefit to giving someone else access to your CC Processor. At that point in time they are no longer penetration testing your systems: they are penetration testing someone else's systems that you happen to use. Indeed, giving out access credentials in such a way likely violates the terms of service that you signed when you started using your CC Processor (not to mention the other systems they are requesting access to). So unless you have permission from your CC Processor to hand your credentials to a security auditing company (hint: they would never give you permission), giving them that access is a huge liability.

Many others here have done a great job articulating the differences between white-box and black-box testing. It is certainly true that the more access you give security auditors, the more effectively they can do their jobs. However, increased access comes with increases costs: both because they charge more for a more thorough vetting, and also increased costs in terms of increased liability and increased trust you have to extend to this company and their employees. You are talking about freely giving them complete control over all of your companies systems. I can't imagine any circumstances under which I would agree to that.

How should I proceed?

Don't proceed with them. The way they act is unprofessional. Pentests carry risks for both parties, and it doesn't seem they did anything to address them.

First, you should absolutely not hand anything over without a written contract (including an NDA). It's surprising they routinely do business like that. How do they know the exact scope? Under which terms do they get paid? Will they just clam they're "done" at some point or is there a timetable? Do you get a proper report? Who pays if they cause damage? Are they insured in case they lose your credentials to a third party? How will you know if a future breach is part of the test or an actual attack by someone else? Even if you trust them, these questions should certainly be answered before you kick off a pentest.

And it's not just you, they are putting themselves at risk. If you never clarified the scope, they might be attacking some of your systems without permission, with potential legal implications.

I assumed it would mostly be black box.

Both black and white box tests are common and each approach has its own advantages. But if the mode of testing never came up, it seems like there has never been a discussion about what should be achieved by conducting a pentest in the first place. A professional contractor would have assisted you with figuring out the right conditions and methods.

(One great first question to a potential contractor is asking them for a sample pentest report. It will give you an initial idea about how they work and what results you may expect.)

Prior to any penetration test there should be a Scoping and Rules of Engagement document(s) that is signed by both parties. These documents should describe in detail what will be tested and what methods have been agreed upon by your company and the contractor. If you have not gone through this discussion with your contractor, discontinue the engagement and seek other professionals.

As a penetration tester, I have asked companies to provide accounts or laptops that they would provision a normal user. This allows to test from a malicious employee perspective. However, this is all agreed upon prior to the test in the Scoping and Rules of Engagement.

Just my 2cents.