To my recollection, all information is "required" to move on to the next screen. But what you place in most all spots can be edited later. The things I would imagine are hard to edit later would be name, address, email, DOB/age and gender. Although, I've got to imagine even address/email may be editable at a later time, but I highly doubt name, DOB/age, and gender are that easy to edit at a later time (and may even pre-fill based on your runDisney profile). With that being said, don't just completely skip the other questions. Because from these images, they have the classic "*" next to them to indicate that the process might likely bounce you back to doing the same page again when missing questions.
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So if you're aiming to save a few seconds on registration, just submit an estimate above 2:00 hrs on POT. For a t-shirt size, just select something quickly and edit later. Have your CC ready to enter.
In all likelihood, it's getting into the actual registration page that is going to take the precious time. In the past, they didn't save your bib once the registration page started. But the registration itself takes maybe 1-2 minutes if you're quick and doing a solo one. The time it takes to actually get from queue to the registration page can be 5, 10, 20 minutes, and that's where the time is most likely lost. So my advice is several devices, with several different browsers, opening the link at times before and after the registration window opens. Maximize your chances and minimize the time waiting in the queue.