Battery indicator is only shown once the device is booting up into the main menu. Or getting into the main manu from the rest of its activities (reading the books, etc.).
The symbol is not shown elsewhere, in particular when reading the book, which sometimes causes some nerves when it shuts down for battery empty reasons
The battery cannot be simply soldered out/in for it uses a flatcable. It needs some special tools and skills and a battery that fits the Sony. I did not open my T2 so the info I got comes from internet.
However, make sure you use the right cable to charge it. The Sony is extremely picky about the cable and the charger - one needs the right combination, or use a Sony/Samsung branded cable and use the computer. It may wake up from dead.