Wi-fi is free and unlimited. The airport address is called FREE.WIFI and after connecting you have to skip two ads.
Before and after security you will find several small restaurants and bistros, the prices here are 2-3 times higher than outside the airport.
There is a baggage room in the arrivals area of the airport. It is open 24 hours and the price for one day is 120 uah.
There are several ATMs in the public area of the concourse, most of them belong to Euronet, avoid these due to the high fees. However, there are also ATMs of regular Ukrainian banks, which charge withdrawal fees as well, but not as high as Euronet ATMs.