On issue #1, it certainly takes the body time to implement changes. However, with “poor” nutrition and an eating change, it is hard to say what may have to be corrected.
For example, if someone were to start lifting, the body would have to build muscles and probably strengthen tendons, ligaments and bones. With appropriate nutrients muscles will adjust quickly while the others will lag behind.
I generally think of non-muscle changes in terms of weeks and months. For example, some foods and supplements change the way the body works in minor ways. Perhaps gene expression is altered or certain optimizations are prefered - as in fish oil causing cardio adaptations.
These types of changes also won’t be instant, as the body will have to operate under the new conditions for some period of time for whatever changes it is making to propagate.
Also, if you had some subclinical chronic issues that were exacerbated by poor nutrition, that your body could fix with improved eating habits, more antioxidants and required nutrients for example, then again it would certainly take time for the issues to be halted and then for any problems that were caused by those issues to slowly alleviate.
However, with respect to fat loss, if you are consuming less calories that you are expending, you’ll burn something off. While energy consumption is a fast process we carry incredibly large reserves considering our daily needs.