Thank you for the new information.
It sounds like you have a vacuum leak as they are the most common causes of the 4 Lambda codes you have. This can be confirmed by looking at your fuel trims. Each bank will have a short term and a long term fuel trim, so there are 4 in total. The OBD2 scanner will give the values in %. The normal range for the long term fuel trims is +/- 4%. -4% means you are running rich (negative) and 4% means you are running lean (positive). Once your fuel trims get to >-/+8% then you have problems to find.
Read these threads:
Introduction It took me a long time to understand fuel trims, despite excellent videos by 50skid and excellent posts by JFOJ. I think I have a handle on them now, so I thought I would try to explain them as I understand them, and either help someone and/or get corrected. Here is my shot. Theory...
www.e46fanatics.com
There are so many requests for solving problems that usually start with "do a smoke test for vacuum leaks" that there's a real need to have a single thread dedicated to smoke testing. Then we can just post the link to this thread when someone needs smoke testing info. Please chime in with your...
www.e46fanatics.com
You can also get lean fuel trims from an exhaust leak before or at the Pre-Cat O2 sensors. A smoke test will not find these leaks. As you have had your exhaust manifold apart, check for exhaust leaks if a smoke test does not find any problems.
True "Limp Mode" can come from the Automatic EGS module and the ABS module. Some people get performance issues which they think is limp mode, but is just really bad fuel trims. As you do have the ABS and Traction control lights up, you'll need to get a scanner with BMW software are read the trouble codes from the ABS module. It may give you some good clues. See this thread:
How to Install BMW Standard Tools
Does the Mishimoto cold air intake have an oiled air filter? Sometimes people over oil the filters and the oil contaminates the MAF sensor. About the only time cleaning a BMW MAF does any good is when there is an over oiled air filter in a cold air intake. The oil on the MAF will make it under report. This causes lean conditions. As you have a cold air intake, a quick test is to un-plug the MAF as see if the engine runs OK. If it does, then clean your MAF. If that does not improve things, the search for vacuum leaks.
Your BMW does not have an EGR valve. I'm guessing that you are referring to the DISA valve on the side of the inlet manifold.