On eBay, I accepted an offer and the guy has yet to pay. Meanwhile, it was a pretty hot item and my item is not listed. How long must I wait to cancel the order without getting any negative consequences from eBay or the algorithm?

Four days, but that window is extended if you send an invoice so don't send an invoice. eBay sends payment reminders so an invoice is not needed. Read more about unpaid item process here:https://www.ebay.com/help/policies/payment-policies/unpaid-item-policy?id=4271