Should I buy this (gently) used, 15 year old, helmet?
No. It is safety gear – buy a new one.

The old helmet might make a good pot for a hanging plant but it is more likely to fail dramatically in your moment of need.

The straps would probably come right with a soak in water, but the polystychrene is the functional part and it has failed with age.  

It might fill a legal requirement if your location mandates helmet wearing, but it probably won't provide sufficient protection.