I very recently purchased an item on the PlayStation Store and removed my billing information immediately after the purchase was downloaded onto my console. Will this by any chance cause any problems for say, my account being charged or being able to pay off my credit card when the charge appears?
No. Sony still has a copy of your credit card information in the billing system. Any past transactions will still be completed even if you remove your billing information from your PSN profile. It just won't be available for use for future transactions.