Yes, the following batteries can be charged in the Sony BC-TRX, Cyber-shot Battery Charger: NP-BX1, NP-BN1, NP-BN, NP-FG1/BG1, NP-FD1/BD1/FT1, NP-FR1 and NP-BK1. Or, in short, for all X-/N-/G-/K-/D-/T- and R-series batteries.

Enclosed is the charger incl. battery: Sony BC-TRX, Cyber-shot battery charger incl. NP-BX1 battery (charger, battery)

unfortunately no - Sony batteries are usually not compatible.