Life in the stronghold goes its own course, no matter of your progress in the main storyline. Event occurrence is strictly connected to passing of days in the game. You should react differently on each of few different event types.
Most of your attention is required when a group of enemies, usually bandits or faction members that don't like you, us coming to the fortress. Usually, you will be informed about their attack three days before they come. You can order your hirelings and companions that reside in the stronghold to prepare defense. This order doesn't cost much, but virtually always few buildings are destroyed during battle. Rebuilding them not only take few days, but cost thousands of coins as well. A better solution is to return to the stronghold and face enemy by your own. You lose some time on that, but save lots of gold. After every attack you must rebuild basic infrastructure, which costs few hundred gold. If player doesn't have enough money, a loan is taken automatically which then is paid by money generated from taxes. Player can pay the loan automatically as well.
From time to time, traveling merchants will visit you. The higher your prestige level, the more often it will happen. They usually offer you one very good item for not so small price. Usually it costs 3000 coins, which is two or three times less than if you would like to buy the same item at normal merchant. Before deciding, check if that item will be useful for any of your party members. Bought items can be found in chest in the keep.
Sometimes you are given an opportunity to send one of your companions with a mission. It usually takes few days and is profitable for more than one reason. Companion receives experience, you gain gold, and in some cases even prestige or reputation.
Sometimes an unexpected guest arrives at the stronghold. It might be a lord that was passing nearby and decided to stay for a while in your fortress, thus temporary increasing your prestige. Sadly, it might be a local criminal as well, that will cause both prestige and safety to drop. There are two ways of getting rid of him. You can pay him to get out or order one of your companions to "escort" him out.
You receive information about other events as well. Each week you receive a report which describes how much money have you gathered and how many coins have been robbed from the treasury. If bandits took too much money, it is a sign that you should increase strongholds safety - by placing new buildings or hiring other hirelings. Each weak you receive information about how much does all hirelings cost you as well.
Stronghold gives you access to additional quests. Usually those are quests that focus on eliminating a specific person or group. To be able to take those quests, you must build a Warden's Lodge. This building can be found outside stronghold walls, in the northwest part of the map. Inside you will find Warden Fyrgen who is an intermediary between you and your employers and is responsible for paying rewards. At the same time you can take more than one quest.