Is the prayer of those praying on the upper floor of the mosque valid if they cannot see the imam or the congregants, and only hear the voice of the imam or the loudspeaker, with clarification of the opinion of the four schools of thought?

The Hanafis stipulate, for the validity of the follower's prayer behind the Imam, that there should be no ambiguity regarding the Imam's situation and no difference in location. So, if the Imam is seen, or if those behind him are seen, or if he is heard, or if the one conveying his words is heard, then the ambiguity is removed. And if everyone is in the mosque, the location is truly unified, even if it is spacious.

The rest of the madhhabs (schools of thought) do not differ from the Hanafis in this regard. They explicitly state the validity of the prayer of one who is in the mosque merely by hearing the takbir, even if he does not see the Imam or the congregants.

In summary, one who is in the mosque, even on an upper floor, can validly pray behind the Imam, provided his situation is not ambiguous to him, either by hearing the takbir, or by seeing the Imam, or some of the congregants.