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Yes, basement insulation needs a vapor barrier due to its susceptibility to moisture seeping in from the outside of the house. You should install a moisture barrier before you install insulation or purchase insulation that comes prebuilt with a moisture barrier to avoid water damage in your insulation and costly mold and water remediation expenses. 

According to a report from Energy.gov, radiant barrier installations can save between 5% and 10% on your energy bill each month that your HVAC cooling is in operation. That fact can mean savings of up to more than $325 per year for homes that experience frequent direct sunlight and high summer temperatures. 

Yes, usually you will need some kind of vapor barrier on the exterior walls when the framing is attached to concrete and masonry surfaces.

Doubling the insulation in your home also doubles the R-value of said insulation. In other words, by adding more insulation, you can reduce the heat loss by half. Most homes benefit from increasing insulation. Older homes, in particular tend to have less insulation as is, so doubling your insulation could drastically reduce your energy bills, keep your home more comfortable, and take the strain off your HVAC system.