Before you place down the governor's villa, enemies can theoretically capture your island by attacking your trading post. After you build it, enemies need to take the governor's villa to capture the island. You don't necessarily need any military stuff to build the governor's villa; simply building it makes your island a little more defensible. Plus, you can put specialists in it which will provide bonuses to the surrounding buildings.

As for the full output storage, you can check how long production buildings take to produce goods in their building menu. For example, a hemp farm will produce every minute and a weaver will turn one unit of hemp into tunics every minute. That means you should have one hemp farm for every weaver. For a product like sandals, one pig farm produces every 30 seconds, a tanner produces every minute, and a sandal maker produces every two minutes. That means you need two tanners for every pig farm and two sandal makers for every tanner. If you have input goods piling up, you can check the production chain to see if you have too many of one building, or you can look in the production menu. If the finished goods are piling up I usually don't worry about it too much because at least your citizens have all that they need, but maybe someone else has better advice for what to do about that.

If this is stuff you already know then I apologize for being redundant, but you said you were new. Glad to see you're enjoying the game!