If I made an account on Wikipedia on one IP address but opened it on another, would that create problems?
E.g. If I attempted to open my account on an IP address that had been completely blocked (no editing, no creating new accounts etc.) but I haven't received a block for anything that I have done under my username, will I be blocked on that IP address? If so, is there a way to appeal it?
Yes, it could, depending on the nature of the circumstances. Check out unblocking on the various ways to go about either getting unblocked or getting an exemption.