xvlaze:
So I connect UNO's pins 10, 11, 12, 13, GND and 5V to Pro Mini's RST, 11, 12, 13, GND and Vcc, just like I read in many tutorials.
Ok, here's the deal (I think): Because you started out doing some stuff with ISP programming, you may have uploaded the blink sketch and wiped out the bootloader before you got that error message "programmer not responding: not in sync". So your Pro Mini is in an unknown condition. I recommend burning the bootloader fresh on it using your Uno loaded with the ArduinoISP sketch.
Upload ArduinoISP sketch to Uno
Connect UNO's pins 10, 11, 12, 13, GND and 5V to Pro Mini's RST, 11, 12, 13, GND and Vcc
Connect a 10uF or bigger capacitor to the Uno with the striped or neg lead on GND and pos lead on Reset.
Select on the Tools menu:
Programmer: Arduino as ISP
Board: Pro Mini
Port: port of the Uno
Burn Bootloader
If you get the message Done Burning Bootloader, the Pro Mini is ready. Disconnect everything and connect your Pro Mini to a USB-to-serial adapter and upload a sketch (such as the blink sketch) to it. If you don't have a USB-to-serial adapter, I recommend getting one of these: FTDI Basic Breakout 5V/3.3V With USB cable
If you don't have a USB-to-serial adapter yet, I recommend ordering one, and while you are waiting for it to arrive you should be able to use your Uno. Connect:
Uno Pro Mini
RX RX
TX TX
5V VCC
GND GND
On the Uno connect Reset to GND, this will suspend the processor on the Uno to keep it from interfering with the upload to the Pro Mini. Instead of connecting Reset to GND you could remove the ATmega328P from the Uno, but if you do, be careful not to bend/break the pins.
In the IDE select the Uno port and select the Pro Mini board, compose a sketch and click the upload button. Press and hold the reset button on the Pro Mini. When the IDE changes from Compiling to say Uploading, release the reset button on the Pro Mini.