Yes, a USB charging cable is included in the scope of delivery. You do not need to order a separate cable as the device is supplied with a USB charging cable.
I would have to check, but we stopped using the device. At the lowest rating, the measurement varied so much that we had to fear an oxygen deficiency and only after tests at the doctor's did we find out that it was the device.
Then we bought one for the finger. Not as comfortable, but measurements are better. Subjective opinion.