"Dominated by" means "has as the most noticeable feature".
So, most of the near-5000-kilometer diameter of the planet is its iron core.
Similarly, a very large building is said to "dominate" the skyline, or a vital issue like the economy might "dominate" an election.
"Wrinkled" here just means the surface of the planet has ravines or canyons that (from a great distance) suggest wrinkles on a face or a piece of fabric.
I don't know what "shrinking history" means. Perhaps Mercury is not as old as scientists once believed.
EDIT: Someone apparently claiming to be Paul McCartney points out that "noticeable" could be interpreted as "noticeable on visual inspection". You can barely see Mercury at all, and even if you were close enough to see the surface, you still couldn't see the core. The article means, "If you looked at a cross-sectional diagram of the planet, you would see that Mercury is mostly iron core, with a thin layer of something else on top."