How to connect Arduino Nano with ESP8266 and BMP180?
Connections:

[...]


Rx to Rx
Tx to Tx


That's not gonna fix your problem with initializing the BMP180, but you have to cross the lines, Rx to Tx and Tx to Rx, if you want to get anything on the serial terminal... Besides, your Nano is 5V, your ESP 3.3V. Connecting directly the Nano's Rx/Tx lines at 5V to the ESP's Rx/Tx 3.3V lines might not be very safe.

As for the BMP180, is it rated for 3.3V, or only 5V? If it is 5V only, it might not work on the ESP. Hence the init fail.