What is the ruling on drawing plants, places, landscapes, and imaginary planets of my own creation, and does this constitute imitation of God (mudaahat Allah), given that these things do not exist?

It is not forbidden to draw inanimate objects such as trees and plants, whether real or imaginary. This is the view of the majority of scholars, because the prohibition of drawing is specific to living beings and does not apply to trees and the like. This is indicated by the hadith of Ibn Abbas, may Allah be pleased with them both, and affirmed by the statements of scholars.