Then I think your site will be fine here at DreamHost.
That is certainly not normal. In my time with DreamHost I have only experienced one billing error, when registering a domain using PayPal for payment, and that was in my favour, my account was actually credited with 3x amount extracted from my PayPal account. Of-course, I notified DreamHost and they fixed it up.
Is it possible you submitted two applications? There have been a few reports here on the forums of 'glitches' during the sign-up process, where people are unsure of whether the application went through or not. Although, I am guessing if this happened you would have experienced the dreaded 'credit-card already in system' error.
The approval time for new accounts does vary quite a bit, some are approved within minutes, others take a few days. I am not sure what causes the difference.
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