How to choose a protection diode (power)

  1. Is one diode (either on Vcc or GND) is enough? Which one to choose?

One diode will do the job either on Vcc or GND. But a Diode to GND will shift the GND voltage so if you have another equipment powered with the same battery connected to the arduino that voltage shift can lead to some problem

  1. What type of diode to choose (voltage etc ratings)?

Voltage : the battery voltage
Current : the current you deliver to your board
Power : the current time the voltage drop across the diode (wich is quite low)

  1. I have battery powered device with very low power consuming (most of the time MCU is in "Power down mode" -- around 1uA or less) will diode take some power?

You should take into account the voltage drop across the diode. This voltage drop can be an issue with battery powered equipment. You should choose the diode in the Schottky family as the voltage drop is much lower than in standard diode.