Yes, you can charge the battery with USB-C. It is best to use a 65W USB-C PD charger for the fastest charging time of 2 hours. A normal mobile phone charger (5V/2A) will also work, but will then take approx. 10 hours.
Charger is not included. Depending on the charger you use, the battery will take shorter or longer to charge. With my laptop charger it takes about 2 hours to be fully charged.
Yes, The Battery is compatible with the Soundboks 4 and works with all existing Soundboks speakers, including the Soundboks 4, and even allows you to listen to music at full volume while charging when using the official charger or a USB-C PD compliant power supply with at least 65W.