When a block of ice at zero degrees Celcius melts, the ice absorbs energy from its environment. As the ice is melting, the temperature of the block (remains the same, increase decrease)

I think it remains the same.

A sample of liquid ethyl alcohol is boiling. As more heat is added, the temperature of the liquid alcohol will (remain the same, increase, decrease)
I think it will increase.

what is your question?

whether it remains the same, increase, or decrease.

right on 1, wrong on 2.

As long as ice and water are together (that is SOME ice and SOME water) the temperature of the melting mixture will stay at zero C. After the last molecule of ice as melted, then the temperature of the melt will begin to rise.
Ethyl alcohol, at the boiling point, will continue at the boiling point until all of the liquid alcohol has evaporated. After the last molecule of alcohol has evaporated, added heat will increase the temperature of the alcohol vapor. (It is possible, if heat is added VERY VERY fast for the temperature of the liquid alcohol to rise BECAUSE of insufficient mixing but I don't think that's what the question has in mind.)

For the first question about the block of ice melting, the temperature of the ice actually remains constant at 0 degrees Celsius while it is melting. This is because the energy being absorbed by the ice is used to break the bonds between the water molecules and convert the solid ice into liquid water, rather than increasing the temperature. Once all the ice has melted, further energy input will cause the temperature of the liquid water to increase.

To find the answer to this question without relying on guesswork, one can apply the concept of latent heat of fusion. The specific heat capacity of ice is smaller than that of liquid water. Hence, when heat is added to ice, the increased thermal energy is used to break the intermolecular bonds, resulting in the phase change from a solid to a liquid. During this phase change, known as melting or fusion, the temperature of the substance remains constant. Therefore, the correct answer would be that the temperature of the block of ice remains the same while it is melting.