2010 Cooper Base w/ manual Trans (non Turbo)

My son burn a clutch up getting stuck in the snow. So after a clutch, pressure plate, and a trip to the machine shop it is back together.
Here's my problem. I have a vacuum leak on the drivers side of the head. Found via use of a can of carb cleaner.
I have codes:P3033, P0301, P0302, P0303, P0304. It starts and run normal for about 10 to 13 seconds. Then it starts missing. If I give it gas it will stay running and how I found the that it's on the drivers side.
With Carb Cleaner it runs without missing.

I've looked and I am not finding the leak. It also has or had a oil leak. When I split the trans and motor oil came out so I also did the rear main seal. Now I am thinking it on the forward top side of the motor. A Round looking thing with a vacuum line on it (not leaking)

My first concern if the leak and getting it to run right. I have not looked at the line under the intake, found posts on it and will look in the morning.

 

P3033 should be the IAT. Did you reconnect the sensor on the passenger side front bumper?

My vacuum pump gasket was once leaking really bad. The round thing with the vacuum line on it. The gasket is between the pump and the head. Though not sure if that can become a severe vacuum leak

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That only goes to the brake? So it should not effect the engine...