Thanks for the write up! I used it to start my idler pulley change, but ran into a significant problem.
The pulley you have in your photo, BMW part #11287841228, has an off-center bolt hole and is only compatible with M3's built before 4/29/08.
See here for details. For production dates of 4/29/08 and newer you will need a pulley with a centered bolt hole, BMW part #11287841531.
This stationary idler pulley is also referred to as a "deflection pulley."
Production date up to 4/29/08 on the left, 4/29/08 or later production date part on the right:
Another thing to consider is that the hoses that run below the fan shroud are clipped onto the fan shroud to hold them in place. As you pull up on the fan shroud some of them will not want to come loose easily. You can carefully try to reach below the fan shroud with one hand to loosen or remove them. When you are re-installing the fan shroud you can skip the step of clipping the hoses back in place and with a little luck, you will probably never have a problem, but it's not recommended. I couldn't find a way to re-clip those hoses back into place without removing the belly pan cover below the car. The next time I do this job I'll start by taking off the underbelly cover and unclip the hoses from the fan shroud to start with. Here are some of the clean clip marks on the hoses below. I believe there were two additional clips to the right just out of the photo.
