What are the modes of heat transfer due to a temperature difference?

Statement $A$: Convection involves flow of matter within a fluid due to unequal temperatures of its parts.
Statement $B$: $A$ hot bar placed under a running tap water loses heat due to the effect of convection within water.
Statement $C$: Heat transfer always involves a temperature difference between two systems.

$A$ wall with a cavity consists of two layers of brick separated by a layer of air. All three layers have the same thickness,and the thermal conductivity of the brick is much greater than that of air. The left layer is at a higher temperature than the right layer,and a steady-state condition exists. Which of the following graphs correctly predicts the variation of temperature $T$ with distance $d$ inside the cavity?

The sun,acting as a black body,emits maximum radiation at a wavelength of $0.48 \ \mu m$. The average radius of the sun is $6.96 \times 10^{8} \ m$. The Stefan-Boltzmann constant is $5.67 \times 10^{-8} \ W/m^2K^4$ and Wien's constant is $0.293 \ cm \cdot K$. The decrease in the mass of the sun per second due to radiation is ..... $kg/s$.

In Column-$I$,system surroundings and in Column-$II$ modes of heat transfer are given below. Match the following:

Column-$I$	Column-$II$
$(a)$ Cup of hot tea in room	$(i)$ Forced convection
$(b)$ Substance kept near fire	$(ii)$ Natural convection
	$(iii)$ Conduction
	$(iv)$ Radiation

In the variable state,the rate of flow of heat is controlled by