No. Sony SRS-XB10 does not have the inbuilt FM radio but you can attach it to your phone via Aux cable and can play FM radio via your phone.
Yes, Sony SRS-XB10 does have the inbuilt microphone.
It takes about 2 hours to fully charge the Sony SRS-XB10 speaker.
Sony SRS-XB10 Wireless Bluetooth speaker comes with 1400 mAh Li-Polymer battery, which offers about 16 hours of play time with a single charge.