When exiting the submerged capsule, the gal pushes the hatch outward. The water pressure would make this absolutely impossible. Plus a hatch on a spaceship or aircraft is designed to open inwards so that the positive interior pressure keeps it shut.
When Louise mentions her "TSH levels", she is more than likely referencing "FSH levels" as they are far more relative to female fertility.
The "tree" shown is actually a fern. A real tree as a sapling sprout would have been a more convincing replacement.