The choice of verb tense forms is governed by the speaker's degree of belief in the possibility of the scenario's coming to pass.
In item 1, if the speaker believes it possible that all diseases in the world will be eradicated, the if-clause will have the present tense "are eradicated" and the result clause will have "will live to be":
1b. How old WILL human beings live to be if all diseases in the world ARE completely eradicated?
If, in contrast, the speaker believes it unlikely that all diseases in the world will be eradicated, the speaker will use "were eradicated." The verb form in the main clause would be "would live to be" The use of the past tense form "were eradicated" makes the question hypothetical, putting it into the realm of conjecture. This speaker does not expect a total eradication of all diseases in the world. In this case the question would be
1.a. How old WOULD human beings live to be if all diseases in the world WERE completely eradicated?
In the second sentence of Item 2, there's an implied if-idea: "if dinosaurs EXISTED" (which they don't). The question must be about a hypothetical scenario. Therefore the appropriate verb form is "would be":
Do you think it WOULD BE possible for dinosaurs and human beings to coexist on the same planet [if dinosaurs existed]?
The question "Do you think it IS possible for (X) and (Y) to exist on the same planet?" would carry the assumption that(X) (dinosaurs) and (Y) (human beings) do in fact exist, or that they may exist in the future. We're pretty sure about human beings existing (at least now, and, we hope, in the future). It's clear, however, that dinosaurs don't exist today, and, according to all available evidence, aren't likely to exist in the future.