If a basement is unfinished, does it still need foundation insulation?
Yes, unless the floor above is insulated. Even if used only for storage and heating and cooling equipment, the basement is thermally connected to the rest of the house.

Is floor insulation above a basement or a crawlspace an alternative to foundation insulation?
Yes, but keep in mind that pipes, ducts and HVAC equipment located in the basement would then need to be insulated to protect pipes from freezing. Sometimes these can be grouped in a small area with insulated walls while the floor above the rest of the basement is insulated.

Doesn’t placing insulation on the exterior improve energy performance?
If the basement incorporates passive solar design with a significant amount of south-facing windows, exterior insulation will be beneficial, provided the walls are exposed to solar gain. In a typical basement, the energy savings are negligible.