Keep seeing the same questions with no solutions to the same questions I had. I wanted to take the liberty of making a short FAQ to respond to some of the questions.

Q1. How to deal with corruption?
A1: Its based on administration efficiency. Administration efficiency is tied to your influence and executive branch positions of your party (I think). What I do know for certain is that its tied to your income/expense sliders. The more to the right they are(the more expenses), the less effective the administration is and more money is lost to corruption

Q2. How to update army weapons? They don't show up when I do research.

A2: Assuming you have done research... Pick any faction weapon such as musket or carbine, equip it on your soldiers and once the battle starts it will automatically be upgraded (To test this out, go find someone to fight, start the battle and kill one of your men... He will drop the upgraded version of the weapon you gave him)

Q3. Vassals do not follow me when I ask my companion to call them!

A3: Your companions are incompetent at sending messengers. Best way to go about it is to find a roaming general of your faction and tell him you want to start a campaign. Now everyone will follow you until dismissed.