You’re right EGTC. Those are the pre-landing checks conducted downwind.
As for the cooling down procedure, leave the engine running for several minutes? Who taught you this? It’s a PA-28, we only allow 30 seconds in a Q400 which has been running at 660°c for the last 2hrs.
I still do instructing, and my students are always taught as per the AOM. What does it say in yours UKAVIATOR? It won’t be “several” minutes that’s for sure.