I developing battery-powered device based on PocketBeagle + Bela mini + Linux 4.4.113-ti-xenomai-r149.1.
I connect button to some GPIO for wake-up system and use "echo mem > /sys/power/state" to put system into suspend.

When I put "echo mem > /sys/power/state" my system decrease power consumption to ~50 mA, but when I press to button the system is not wake up.

Is my kernel support suspend to RAM or other mode (standby) ?
How to configure pin to wake up?

No idea about this. The kernel we have is a bit old and the PocketBeagle is not fully supported (for instance: shutdown -h now does not actually turn off the LED). I have an experimental build of the 4.14 kernel here that you could try. If this also fails, then try to install one of the beagleboard.org images and see if it works there, then we can look into how to backport that