As for what they say, I refer to the declaration that Iran will destroy Israel, and that Hamas will not take any negotiations to be binding upon them.

Yes. I think they are lying. Just as I think the government of Israel is lying when it says it is willing to consider the possibility of an independent Palestinian state, and the US government pretty much every time it says anything at all. The people you are talking about are trying to sway the opinions of their target audiences in order to solidify their hold on power in their own countries, and they will say whatever it takes to accomplish this goal. As will the governments of Israel and the US.