What maximum number of buttons i can connect to Arduino (100 buttons and more)
"Is it possible to connect something like 100 buttons to one arduino nano, by using this classic method (or other possible cases)? "

Yes. to connect more than 100 inputs you can Charlieplex 11 of the arduino uno input buttons (this will actually give more than 100 inputs,110 to be exact) . This requires no extra ICs to do. Just still using resistors,diodes and more than 100 input buttons-using 11 arduino uno digital inputs. 

If you want to use IC you can bitbang the 100 inputs using shiftin() see https://www.arduino.cc/en/Reference/ShiftIn

PS2 keyboard (As Dave Tweedy suggested) is less flexible regarding scalibility (eg if you want 200 inputs you just daisy chain some IC together) and probably more programming work than using the IC method above.