>>528557953
Night battles are not counted as a new battle.
Fatigue/morale affects the accuracy of your umas and the cap on damage they will take. It has no effect on leg breaking, but try not to race with fatigued umas.
Formation
Before the battle starts you can choose a formation if you have 4 or more ships in your fleet.

Formation 1: Line Ahead (単縦陣) - Offensive formation that maximizes speed, accuracy and mental damage. Weak against Diamond. Lowest chance of flag uma protection. Default formation for 3 or less umas.
Formation 2: Double Line (複縦陣) - Balanced formation that gives the highest accuracy, but less front vision than line ahead. Maneuvering has moderate accuracy. Moderately weak against Echelon. Available at 4 umas.
Formation 3: Diamond (輪形陣) - Anti-air formation that decreases accuracy and mental damage. Strong against Line Ahead, and very strong against aircraft. Very bad against guns. This formation also increases the chance that other umas will take damage instead of your flag uma (flag uma protection). Available at 5 umas.
Formation 4: Echelon (梯形陣) - This formation is the least well-tested, but it is thought to be a defensive formation. Somewhat strong against Double Liners. Bad for foreign umas and surface combat. Available at 4 umas.
Formation 5: Line Abreast (単横陣) - The best anti-Echelon formation, but greatly decreases mental damage. Very bad for foreign umas. Available at 4 umas.
Unless you are fighting foreigners, line ahead and double line are almost always good choices. Fleets heavily reliant on foreigner for damage should choose line ahead.