1) If you feel you are mastering the battlefield you may try a pursue but beware counterattacks or low speed units that are far behind the first line. Pursuing is just an option that may be used if the situation is right. Try it sometimes so you can do your own experience with it!
2)Losses are part of the war! You can minimize them but they will always happen! Remember that suppressed enemy will be less effective. Use artillery fire to suppress them and also try to attack from different route. Use cover to get near the enemy while you screen them with units from far away so you can maximize the effect of the "stumbled upon" attack of the sneaking forces. There are lot of other way to try to minimize the losses but sometimes triing it will maximize them!