Is the Apple online purchase system down for some reason?

<<. I think the online purchase system of Apple is just not working for Apple Cards. >>

Hundreds of thousands of satisfied buyers of stuff from Apple say the Apple Card is not a problem.

That does not sound like a satisfactory answer.

Call again and be more assertive. If the agent you are speaking to cannot answer your questions to your satisfaction, ask to speak to a supervisor.

and you can also provide feedback on this page, but you will not get answers there:

Product Feedback - Apple

<< While talking to customer support, nobody is able to explain the reason or can explain why the status “processing” means. >>

"Processing" is the state your order stays in after it is accepted, and while factory builds and tests it. the next stage is "preparing to ship", where it is boxed and moved to the shipping dock. "Shipped" means it got onto a pallet and onto truck with dozens of others and left for the airport.

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It sounds like the person you spoke with needs to be re-trained.

It's their system. They are the experts. Call again and be more assertive. If the agent you are speaking to cannot answer your questions, ask to speak to a supervisor.