The heat from the hot water is transferred to the ice, making
the ice heat faster, thus causing it to return to room temperature
faster, making it melt faster.
Will water boil faster if there is less of it?
A small amount of water will reach it's boiling point sooner
than a large amount of water. It will not boil faster.
Does the water boil faster with more water?
Slower, the more water, the more time required to reach boiling
temp.