Plain version: HSA money goes in with a tax break and comes out tax free, as long as it is spent on qualified medical expenses. The owner can take money out at any time; the tax result depends on what it pays for.
Non-medical withdrawals: the amount is taxable income and also bears a 20% additional tax, unless the distribution is made after the holder becomes disabled, reaches age 65 or dies. Age 59½ plays no role in HSA rules. Even without the additional tax, a non-medical distribution is still taxable income. Example: at age 50, not disabled, Jay takes $1,500 for a new TV. He adds $1,500 to income and owes 20% × $1,500 = $300 more.
Premiums: HSA money generally cannot buy insurance. The exceptions are long-term care insurance, continuation coverage such as COBRA, health coverage while receiving unemployment compensation and, at age 65 or older, Medicare and other health coverage. Premiums for a Medicare supplement (Medigap) policy are expressly left out, even after 65.
At death:
Spouse as beneficiary: the spouse may treat the account as his or her own HSA.
Anyone else: the account stops being an HSA, and its fair market value is taxable to the beneficiary in the year of death. The amount is reduced by the decedent's qualified medical expenses that the beneficiary pays within 1 year after death.
California is different. Federally, employer HSA contributions are excluded from the employee's income. California's Revenue and Taxation Code says the federal provision on employer HSA contributions, Internal Revenue Code section 106(d), shall not apply (Rev. & Tax. Code §17131.4(a)), so there is no matching California exclusion. Do not assume federal and California HSA rules match.