Is the statement made by the speaker: "Shall we stone Allah, blessed and exalted be His remembrance?" considered disbelief, and is he who says that this statement is disbelief considered an unbeliever?

The word mentioned is vile, and it appears that the speaker uttered it in the manner of a rhetorical question (istifham inkari), not intending that it was a reality or permissible concerning Allah. Therefore, he does not become an unbeliever (kafir) by that. Similarly, you did not become an unbeliever by your statement, but you erred in your haste to judge him as an unbeliever. Both of you should avoid discussions that may lead to sin.