How long will the battery charge last?

A Shimano BT-DN110 battery should last for at least 2000km per charge. When used normally you can expect to get about 2500-3000km of riding out of a single charge, depending on how often you shift and how you shift.

A Di2 front derailleur uses about 4 times more power than a rear derailleur will per shift.

12-speed systems generally go about 1000-1500km between charges, but again, this depends on how the system is wired or not, and shifting habits.