Can I have one device set up with HomeKit and Alexa at the same time e.g. a motion sensor, or a smart plug?
I must stress I am asking whether it is possible to set up the device with the two services at the same time.
Yes, it's perfectly possible.
As and example, I have a set of IKEA Tradfri lights that are controlled by Alexa and Google Assistant at the same time. If I had an Apple device I could add Homekit support at well.
The limiting factor is which of the systems the device manufacturer chooses to support.
Yes, providing the device provides it's own control infrastructure. The model is (roughly):
The exception to this model might be where a device uses one of your system hubs to provide it's connectivity. In this case, you're relying on one integrator exposing locally connected devices to a competitor.
You can refer to this question for a general idea of how devices connect together. An endpoint may have a direct network connection (for example if it has WiFi), in which case many services can establish a connection. If the endpoint only uses bluetooth or ZigBee then some sort of hub is needed. Of course, this hub can be a device you provide if the protocols are open.