Running rough and misfiring randomly when first started, vacuum diagram needed?

Hello, here is the vacuum diagram which is mostly Evap hoses and PCV. The Evap canister purge valve pulls vapor from the gas tank into the Intake manifold to be burned. Blocking off some of these hoses or lines can help to see if they are leaking. If there are any leaks from the gas tank up to the engine, it will be a vacuum leak, but it will come through the canister purge valve when it is commanded open by the engine computer for normal operation. But these are known for vacuum leaks at the Intake manifold gaskets. Most of these Intake manifolds are made of plastic and the gaskets don't seal well or last the life of the engine.
A safe way to check the Intake manifold is just to use a spray bottle and water. When the engine is running, spray around the upper and lower sections of the intake manifold. If it is leaking, you will hear the water being sucked in through the vacuum leak where the gasket has failed. But below is a guide as well to help find any leaks. We will use a smoke machine in most cases, if available. Water will work, the guide below shows using Carb Cleaner, just be careful with carb cleaner around spark plug wires or ignition coils.
The second diagram shows the Evap system, it will still have the same components if you don't have dual gas tanks.

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge