also is there time limit in the line battles
Probably 30 minutes, but I doubt one round would last that long.
For a city siege it is until the attacking army withdraws or the defending army surrenders.
If it lasts more then an hour the attacking army will automatically withdraw for the night.
If a nation go's into debt solders will begin to desert, which is very likely as a nation has only that cities income during the siege while all roads are blocked.