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

R-30 insulation is better for higher thermal resistance, but whether it’s "better" depends on the application. R-30 is much thicker and suited for areas like attics or floors in cold climates, where more insulation is required. R-13, on the other hand, is thinner and works well for 2x4 walls or milder climates where less insulation is sufficient. Choosing between R-13 and R-30 depends on the area being insulated and the climate. For example, R-30 provides more insulation but may not fit everywhere in your home.

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. 

Natural fiber batts and spray foam insulation both work great for soundproofing. Newer materials, such as hemp batts, are more expensive but more effective for insulation and sound blocking. They are also more sustainable. There is also a professional system called Blow-In Blanket Insulation (BIBS) that is soundproof and moisture-resistant. However, BIBS must be installed professionally and can be a costly investment.