Now my next wish is to reduce it's power consumption while keeping the reaction latency low (it needs to react to radio messages).
Well, that's everyone's dream, unfortunately it is impossible.
decrease the consumption with some configuration in BitCloud, is this possible at all?
No, power consumption in active listening mode is determined by the power consumption of the correlator in the receiver. It is a fixed number, and unlike TX power can't be changed at all.
You did not say what radio you are using, but newer radios, like AT86RF233 support smart receive modes, so they consume about half as much as the regular radio.
configure it as End Device, and put into sleep. However in this case how much time is the wakeup? I need 1 second react time worst case. Do you think is possible?
Depends on how many devices you have in the network. Wake up process of the ED is traffic-intensive, so if you have more than 3-5 devices, then they will just step on each other trying to wake up every second.
configure it as End Device without sleeping, and just because of this, can I expect lower consumption (because EDs have limited functionality by design than Routers)?
Nope, again, all the power consumption in the receive mode comes from the receiver itself. If you want to react to the frame, you need to receive it first