Why is it important for an engineer who is designing a new home-cooling/heating system to have knowledge about the transfer of heat?

Cooling and heating system involves the collection and dissipation of heat appropriately. Heat gradient is important for heat transfer between systems because heat travels from the warmer system to the cooler system. The right medium for heat transfer is also important for this exchange – A good conductor of heat is required.

"record the time to complete a chemical reaction" would most likely be part of a lab procedure.

geosphere and hydrosphere.

this is because the geosphere has to do with geological events, while the hydrosphere controls all water on earth.