I want to make some home-automation using arduino nano with I2C. Am I able to use CAT 5e cable for power and I2C? I've read, that I2C over 20 meters is OK using 10 kHz bus-frequency.
Is there anything else, I need to think of?
Wire capacitance is the killer for I2C distance. Twisted pairs are a large capacitor. Power can be on a twisted pair, but you will have line losses depending on the distance. POE usually injects 5.5V to get 5V at the other end.
I2C was originally developed by Phillips for television receivers for a CPU to communicate with peripheral chips without requiring a lot of address and data lines on the PCB. It was never intended as a long-distance data solution, though many of us do so.
From the specifications:
"The maximum capacitive load for each bus line is 400pf."
"The maximum bus capacitance allowable may vary from this value depending on the actual operating voltage and frequency of the application. Section 7.2 discusses techniques for coping with higher bus capacitances."
20 meters would be way out of spec, so try it on the bench before running all your wires.
It looks like you want to do home automation the hard way. Running wires. Personally, I prefer MQTT over WiFi.