Is what was mentioned about the discussion regarding the arbitration of God's law, or mocking natural phenomena, considered mockery of God's cosmic signs, and does it fall under the ruling of apostasy?

You must turn away from misgivings and ignore them completely. As for the ugly word uttered by the brother, he must repent from it. The second word is not a mockery of Allah's verses. If a person falls into apostasy without realizing it, then general repentance forgives all his sins, known and unknown. The conclusion is to resist misgivings and not yield to them.