Early ideas on the classification of life recognized all organisms as belonging to one of two fundamental lineages−prokaryotes or eukaryotes. Is this view compatible with either of the hypotheses illustrated above? Explain.

No, because each hypothesis presents prokaryotes as two separate groups.

you did not attach the discourse, but i assume it to be the discourse on the origin and basis of inequality among men (the original titile in french is: "discours sur l'origine et les fondements de l'inégalité parmi les hommes"), also know as "second discourse". in this discourse, jean-jacques rousseau emphasizes that private property is the basis of all inequalities.

therefore, what enabled the old regime to maintain as long as it did was private property.

the transfer for conduction is the heat transfering from the liquid to the spoon

the transfer for convection is the heat rising from the liquid to the air

the transfer for radiation is the heat going through the sides of the cup and to the air

at least that is what i would do