1. He stooped down to pick up a block.

Question

2. He bent down to pick up a block.
3. He rounded his body to pick up a block.

(Can we use all the verbs? Do they have the same meaning? Which one is commonly used?)

Answer 1

1 and 2 are correct. They mean the same thing. Both are commonly used.
3 is grammatically correct, but would be an unusual way of saying he bent or stooped. We would not say that. We might say he "bent over" or "stooped over" instead of "down", all meaning the same thing, and commonly used.