I normally don't use any of the BMW specific software to see live data. Instead I use an app called Torque with either my Android tablets or Android phones.

I keep an OBD II bluetooth reader in the car at all time and if I want to check something out, I always have my phone on hand.

IAT has a big impact on the MAF accuracy and the engine fuel control.

Some engines have a 3 wire MAF with the IAT in the intake between #3 & #4 intake runner. Not sure if the E53 was like some of the other cars with later versions having a 5 wire MAF with the IAT as part of the MAF.

MAF reading also sounds very high, over reporting, which will cause more fuel to be added to the engine. Most 3.0l will have a MAF reading of 3.6 g/s in park/neutral @ 700 RPM.

If your MAF reading is really in the 7+ g/s range, you have a problem, but also make sure the IAT problem is not impacting the MAF reading/conversion. IAT readings also impact ignition timing as well. I would bet your LTFT are in the negative range, which they should not be.

Suggest you consider the OBDFusion App, $1 cheaper than Torque and not at buggy. OBDFusion along with the VeePeak BT interface from Amazon is less than $20. OBDFusion is also available for iProducts, the App and interface for an iProduct platform is typically under $30. iProducts typically require a Wifi interface rather than a BT interface.

You can also use the App to Log the O2 sensors and this will show you what kind of health the catalytic converters are in, you may have already done damage and caused them to melt down. Typically you need an exhaust back pressure tester, although a compression tester may work, it usually does not do a very good job at low pressure reading. You can get a proper tester for around $37 - Amazon.com: Tool Aid 33600 Exhaust Back Pressure Tester: Home Improvement

There's a free version for Torque, but I found the app to be very helpful that I brought the Pro Version of Torque to support the developer. I have used it on all of my cars with OBD II and never had a problem with it or found it to be buggy. You can check out the reviews by other users before downloading the app.

I know Torque far too well, I have it because it was around before OBDFusion came out. I have found that Torque has problems Logging O2 sensors and it DOES NOT properly support Wideband O2 sensors. I have attempted many times to get these issues corrected and the Torque developer is basically NON RESPONSIVE. The developer does not communicate directly with the end user, they only work via the Torque Forums.

I have been using and working with the developer of OBDFusion on many of his products. I have had many exchanges with the OBDFusion developer on bugs, issues and enhancements and OCTech has been very responsive. OBDFusion is also one of the few lower cost, higher performing Apps that has BOTH an Android and iProduct products.

One of the few Apps that will actually Log Fuel System Status and properly supports Wideband O2 sensors.

https://www.obdsoftware.net/

This is not my first rodeo with OBDII tools, I have more money wrapped up in OBDII tools and manufacturer specific software than many people have in their vehicles. OBDFusion is my first go too App/Tool for driveability and Logging.

While many people have Torque Pro and use it, I do not promote or regularly use it due to the bugs and missing features.

I do however promote products that I use and that the vendors properly support. I am in in regular contact with many OBDII tool (consumer and Pro level) and software providers and point out bugs and requesting features and changes to their product lines. I tend to support suppliers that LISTEN to their end users and fix problems with their products.