My city fell without a battle.#
Your last ground unit left on the same turn an enemy walked in. An empty city goes to whoever enters it. Keep one ground unit in every city you care about. See Moving at the same time.
My planes vanished.#
Their city fell. Planes in a city that an enemy takes are destroyed, and planes in a city under attack can be lost along with its garrison. Keep them in a safe rear city: they reach 3 provinces from there.
My whole stack disappeared after a battle.#
It lost and had nowhere safe to fall back to. A stack that moved in falls back to where it came from, and a stack that was standing still falls back to a neighboring province your team owns. Either way the province must have no enemy in it. With nowhere safe to go, the stack is destroyed.
My new units never appeared.#
The city fell during the turn. Builds only happen in a city you held at the start of the turn and still hold at the end. You keep the supplies.
My support or strike did nothing.#
There was no battle in its target province, or the battle was a border clash. Support and strikes only count in battles fought in the province they target. See Artillery.
My armor stopped after one province.#
It entered a mountain, crossed a river, entered forest (which costs armor its whole move), was traveling with slower units, or fought a battle. See Moving at the same time.
The enemy walked straight past my army.#
Stacks only fight when they end a step in the same province, or swap places across the same border in the same step. Two stacks crossing different borders, or arriving a step apart, never meet.
I attacked an empty province, and there was a battle.#
An enemy stack moved in during the same step. Nobody was defending, so both of you fought on attack values.
The odds said one thing and the battle another.#
The odds on your order only count the enemy stacks you can see. Stacks that move in during the same step, and enemy support and strikes, can change the fight. And a 90% battle is still lost one time in ten. See Battles & odds.
The province I left is still mine.#
Yes. A province only changes hands when an enemy's ground units stand in it with none of yours.
My income went down.#
A city changed hands, so its objective bonus started over. Or you lost a city, or a city you captured pays half. See Economy & building.
Two of my stacks became one.#
Your stacks that end the turn in the same province merge into one stack.
My teammate got the province I took.#
When teammates take a province together, it goes to whoever has the most ground units left in it. See Playing with a team.