1) It would help a lot, but not entirely. Heat is transferred through a few basic mechanisms — conduction, convection, and radiative.

Conductive heat transfer happens when energetic (hot) molecules bump into less energetic (colder) molecules, which heats them up. Convection happens when warm material physically moves — like when air blows, or water flows, carrying the heat along with it. If you were to make a vacuum around your home, you’d prevent conduction or convection — because there would be no material for the heat to transfer through! The third mechanism, though, is radiative heat transfer. This is heat that is carried in electromagnetic waves (like light). You know how much hotter it feels in the sun than in the shade? The temperature of the air is no different; the difference is that you are feeling the radiant heat of the sun. (And remember, that heat came all the way from the sun, through the near-vacuum of space…)

One way to reduce radiant heat transfer is literally to use mirrored surfaces that ‘reflect’ the heat away.

NO. Heat is transferred in three ways: 1. conduction by the collision of atoms or by the vibration of the atomic lattice in solids, by 2. advection or the transport of heat by material flow (hot air transport heat upwards) and by 3. radiation. All bodies at temperature greater than 0 kelvin emit photons that carry energy. Now, in a vacuum, methods 1 and 2 cannot operate. But radiation always does!

Heat is defined as energy which is stored as molecular motion—molecules flying around in gases, churning in liquids, or vibrating in solids. Objects gain or lose heat, and therefore molecular motion, in three ways: conduction, convection, and radiation. Conduction and convection both rely on matter surrounding the object. Conduction occurs when an object touches another solid of a different temperature, like touching a hot plate to a cold table. The molecules vibrating in the hot plate bump against the molecules in the cold table and transfer heat until the plate and the table are at the same temperature. In convection, the surrounding material is a fluid instead of a solid, like submerging the hot plate in a bucket of cold water. Now, the molecules in the water can take energy from the plate and get swept away, letting new cold water molecules interact with the plate.

Finally, radiation is the transfer of heat energy by emitting light. All objects emit light, but whether you can see the light depends on the temperature of the object. At room temperature, the light emitted is infrared, which is not visible to humans. As an object gets hotter, it begins to emit light that we can see, which is why molten metal glows. Even hotter, and the object will emit ultraviolet light (which is why too much sun exposure can give you a sunburn).

Since conduction and convection depend on material surrounding the object, they would not occur if your house was in a vacuum. However, the house would still slowly heat up or cool down due to radiation.

It's true that heat cannot conduct through vacuum, since conduction only happens when molecules collide. In fact, thermos containers and some insulated windows trap a layer of vacuum between two walls (perhaps glass or metal) to reduce heat transfer by conduction.

But even if you could prevent all heat conduction, there is another way to transfer heat: radiation. All solid objects release heat through thermal radiation, which can travel through vacuum. Black objects radiate more heat, as do hot objects. If an object becomes extremely hot, it even starts to glow from all of the energy it is radiating. We call that object incandescent, and this is how incandescent light bulbs work.

The light from the sun is also due to incandescence, in this case from the incandescent plasma on its surface. So even a vacuum-sealed home would receive heat energy from sunlight or other radiation.