I can try to help you here. I don't know what you think the errors shown mean (perhaps you should have added the message meaning and why it led you to think the controller is at fault): I'm not going to look them up for you on this occasion.
The Pace 250 is a Vietnamese-assembled bike from a company based in the US that has been deliberately limited to 250 watts & 15mph, suitable for the UK and EU market, for the distributor, Brick Lane Bikes. As far as I am aware, the US versions of this bike have a 350W nominal output and are limited to 20mph. Newer versions have a Bafang motor but all the connections are the same as the older version with the heavier motor from a different manufacturer.
My first port of call would not have been Alibaba for a replacement controller: you should have gone to BLB: they have some stock of spare parts and the direct link to the manufacturer.
The biggest problem when buying the chinese controllers is that you don't know what system they are designed to support. If you have the motor and battery connections OK on your 3rd party controller, you could replace your display/contoller and brake levers to match the connections on your new controller, if you can find the matching parts. If you open the casing of both controllers, you may be able to establish where wires should be soldered to get the effect you want: usually the circuit boards are labelled. However, if you are confident enough to do that, you may also be competent enough to diagnose the faulty components on the existing controller board and solder in a replacement.
Ultimately it is my opinion that you have made a mistake buying the 3rd party controller and you should either get a replacement from the distributor or manufacturer that is correct for your application, or try again now you know what connectors you need, to find another controller that you can compare photos of with your original unit.
The biggest problem with many of these bikes is the incompatibility between various 3rd party components that make up the system. There are far more variables trying to replace parts from these systems if they are not supported any longer by the bicycle manufacturer (specifically thinking of some of the early brands that are now defunct). Keeping some of these bikes on the road is proving to be quite challenging.
You are in a good position because the bike is still currently available and the manufacturer and distributor are good to deal with. Should that ever change, your situation would involve more work on your part to reach a solution.