Connected the USB-cp2102 stick with the computer. Connected tx and rx with tx and rx on the Arduino Leonardo, and the GND and 5V with the Arduino ones.
You cannot upload sketches to the Leonardo using the hardware serial interface, it doesn't have a bootloader that supports this.
In the Arduino IDE, I selected Board "Arduino Leonardo", Port selected the USB-cp2102 one, Programmer: AVR ISP.
Your USB-to-serial converter (CP2102) isn't an AVR ISP, that's another piece of hardware.
Soo you mean, compile sketch I want to upload. Press the reset button, connect power to arduino, release reset and hit immediately the upload button?
No. Connect the Leonardo as usual at the micro USB connector. Press (and hold) the reset button on the Leonardo, push the upload button on the IDE, as soon as the compilation is finished (and the upload should start), release the reset button on the Leonardo. You might need several tries until you get the correct timing but this worked for most people after they got some practice.
An ICSP programmer is a special hardware that you connect to the header more or less in the middle between pin 0 and pin A5 (6 pins). The cheapest on the market are usually of type USBtiny. With such a programmer you can get your Leonardo to life again for sure.