For starters, these codes have nothing to do with each other. I am documenting the parts I had to replace to fix these codes, as I have not been able to find a list of everything that could cause them in one place. I am also new here, so apologies if this belongs somewhere else. I would also encourage anyone who has struggled with their own specific codes to reply with their solutions as well.

Starting with p0456, Small Evap Leak.
Gas Cap - Could be leaking around the seal, but arguably not likely as this wouldn’t be a “small” leak. Part # 16117222391
Leak Detection Pump - Could be failing and throwing false codes. Located behind the rear passenger side wheel well (if your car is LHD) Part # 16136801158 or 16117158983 (Latter for July 2004+ models)
Charcoal Canister - Could be broken, clogged or cracked. Located next to the detection pump. Part # 16136801156 or 16126766392 (Latter for July 2004+)
Purge Valve - Could be broken or disconnected, and can also throw other codes. Located on the passenger side of the intake manifold/intercooler. Part # 13907572086

This can be a very expensive code to fix, however there shouldn’t be an issue running cheaper aftermarket parts in most of these cases. The pump and canister can be quite difficult to remove, so be prepared. Also, be sure to inspect any hoses and wires that go to these parts.

Next up, p2096, Lean condition Bank 1
Exhaust Manifold - Could be leaking from the gasket to the cylinder head or any welds. Pre-Cat has been known to break. Start the car and feel for pressure from these areas before the engine is too hot. Fix via welding.
Throttle Body Gasket - Could be leaking. Follow the tube down from the air filter to find the throttle body. Part # 13547509045
Supercharger Inlet Duct/Gasket - Most likely issue. The plastic welds could be failing after years of heat cycles, or the green gasket could be leaking. We all know where this is located, and we all hate it. Part # 17511524439 and 11610020836
(Be sure to check the two plastic hoses that run from this part, and the plastic PCV hose going into the supercharger as well.)
Intercooler Boots - Could be cracked or broken, or the clamps could be loose. Part # 17517639959 and 17517639960 (Aftermarket silicone boots are available as well)
Intercooler - Could be broken, in my case the car still made boost despite the side of the IC being completely separated so do not rule this out. Part # 11651515368
Bypass Valve - Would likely throw other codes if it fails, but the seal could be leaking. Located under the driver side intercooler horn. Part # 11617568423
Vacuum Line - Could be disconnected or broken, but would likely cause other problems. Runs from the passenger side of the intake manifold to the fuel pressure regulator. Part # 13517515136 (5/32 vacuum hose cut to the same length works as well)
o2 Sensors - Could be giving a false reading. NTK is the OE manufacturer, DO NOT trust aftermarkets. Part # 11780872674
Map and T-Map Sensors - Could be leaking or failing. One is on the front of the intake manifold, one is on the driver side of the head above the thermostat. Part # 12140872648 and 12140872679
Supercharger Horn Gaskets - Could be leaking. Supercharger to horn, or horn to intake manifold. Part # 17511520044 and 17511524319
Intake Manifold Gasket - A fastener could have rattled loose, or the gasket could be leaking. Replace this if you do the horn gaskets. Part # 11611173671
With the labor, cost, and likelihood of the last 3 being an issue, these should be a last resort if nothing else works.

If the exhaust manifold isn’t broken, there will be a vacuum leak anywhere between the throttle body and cylinder head. I should note that any exhaust leaks after the flange will not cause any issues. If you run a boost gauge, make sure whatever port you get your reading from is sealed properly. Non-S models may have different part numbers.

Clearing this code will require special tools such as Bavarian, INPA, ISTA, or BMW specific code readers. I have one called the AUTOPHIX 7810 that was able to clear it. Similar amazon/ebay readers may work as well. Be sure to clear adaptations, as the ECU will continue compensating for the vacuum leak that is no longer there.

 

Good info @BikeRackMini
Thanks!.
Bookmarked.