[NAME]  It's completely fine to use that dock with an XPS 13 9310.  You'll be able to run dual displays up to 1920x1200 each or a single display up to 2560x1440 (or 4K but only at 30 Hz rather than 60 Hz).  In case it makes you feel better, the USB PD spec used for charging is designed to prevent damage.  Very basically, the process involves a negotiation where the power source provides a list of power levels it is able to provide, and then the device on the other end is allowed to choose from that list.  This design prevents the power source from sending a power level that the device on the other end can't handle, and also prevents the device being charged from trying to draw more power than the source is designed to provide.
I recently bought a XPS13 9310, but i'm not sure i can use it with my WD15 dock. Does anyone know if it could damage the battery of my device?
XPS 13 with WD15 Dock