Hi, I'm working on my bachler thesis. Controlling security shutters with Android app. I did it with Arduino UNO and W5100 ethernet shield. Everything is working fine, but I recently got Arduino pro micro(5V) and I was wondering maybe I could make my project smaller and cheaper a little bit. Pro micro has different pins for SPI: Pro Micro & Fio V3 Hookup Guide - SparkFun Learn . So that means I have to change those pins values in libraries?? Maybe someone can explain how to make it work. Thanks 
Pro micro has different pins for SPI
Obviously it has to have different pins for SPI because the uC used in a UNO is ATmega328p and uC used there on the pro micro is a ATmega32u4 usb host enabled uC, the W5100 has been the standard ethernet controller chip on arduino ethernet shield so its going to be supported in the newer versions of the Arduino IDE which support Arduino Leonardo, so you should just be able to compile fine for the micro by selecting Arduino Leonardo in boards section in the Arduino IDE.
The Pro Micro is a small Leonardo. It has many hardware incompatibilities.
The small "Uno" is the 'Pro Mini'. It's 100% pin/software compatible with the Uno.
But...the SPI library should hide the differences from you. If your only hardware dependency is SPI then it should be easy to make it work.