Can your growth plates become closed when you push push it very hard?

Describe hard. There is a type of uncommon fracture that occurs only inside the growth plate but I doubt that is what you mean. The growth plate contains spongy/rubbery cartilage like material and the osteoblasts that forms bone. it is tolerant on the common mechanical stresses of physical activity. In science almost anything is possible.

Unlikely. Would take significant force, and usually a trauma to close a growth plate.