https://news.harvard.edu/gazette/story/2019/09/harvard-group...
The problem is that it a) is tackling a symptom rather than the underlying problem,
b) may encourage "business as usual",
and c) may come with undesirable side effects.
Such as messing with rainfall patterns in the tropics. I imagine people would be a good deal less forgiving of dying because of famine if it was caused by an informed choice by the first world, instead of an unintended consequence of industrialization.
Is there any science fiction around this concept?
Also, regarding your questions. It is possible to adjust the earth's temperature with that method, but aerosols seem to be cheaper. Regarding solving global warming. Kind of. There are some trade-off with sunlight reduction. See https://youtu.be/dSu5sXmsur4 for more detailed information.
Obviously this would have tons of other consequences for the planet, and doesn't account for solar wind pushing the mylar out of position, etc.
If you want to do large scale construction in space you need to get material from outside of a gravity well.