Generally, ebikes should come with a sensor in each lever that cuts off power to the motor when the lever is squeezed. It's kind of an important safety feature, and seems sketchy that your bike doesn't have one. If the electrical wiring harness on the bike has a few spare connectors floating around, then two of them might be for attaching brake sensors. If there isn't anything extra, then perhaps they cheaped out too much on it, and your best bet is to just hope that whatever brakes you install will be strong enough to stop the bike if a malfunction happens and the motor is stuck powering the bike when you don't want it to. If that is the case and the bike has both a throttle and a torque sensor/cadence sensor to activate the motor when pedaling the bike, it might be safest to remove the throttle from the bike to reduce the chance of an accident.

If the current rotors haven't seen a lot of use, you could reuse them with the new brakes, just make sure to clean them with isopropyl and a perfectly clean rag beforehand. On the other hand, cheap rotors are typically quite flexy and easier to knock out of true, so getting nicer rotors can help reduce how often you need to true them.

I haven't actually seen the version of the MT-200 that has brake sensors in person, and can't find that much info online, so I don't know what sort of compatibility they would have with your bike. With the way Shimano typically operates, I would expect them to do some sort of stupid thing to make their levers not directly compatible with ebikes that don't have a Shimano STEPs motor, but the pictures I see show a connector that looks very similar to the connector on my ebike kit. So who knows?

Brake sensors aside, most cheap generic ebikes use post mount calipers, if yours does, the MT200 should fit fine. If your bike uses a different style of brake mount, then you might need adapters to make them fit.