I have a 2013 825I, about 600 hours, second owner, with similar problems. The left front wheel skidded intermitantly mostly when going down a 6% grade. Eventually, that skidding destroyed the CV joint. That skidding ocurred when the air temperatures were 80 degrees or more. Also, it made no difference if the 4WD selector was in 2WD or 4WD. I would stop, backup 20 feet, restart with some success. Keeping a constant speed helps. This wedging is a common Gator problem.
Upon replacement of the CV shaft, no oil came out of the front differential when the shaft was removed. Removing the drain plug showed the front differential was dry.
Replacement of the CV shaft and lubrication did not completely solve the problem. I considered a dragging brake pad to contribute to the problem. I have yet to install new ball joints.
So, I am still working on the problem. I am also working on other PROBLEMS.
Hope this helps.