Is it legal to store physical gold at home in the US? If so, what taxes may be applied on the gold held at home, in form of both jewelry or raw gold?
The executive order 6102 has been repealed and there's no prohibition on owning and possessing gold in the US. Taxes are paid on income, and gold bullions, coins, and bars are treated as collectibles for income tax purposes. Gain on sale of collectibles is taxed at fixed 28% rate (IRC Section 1(h)(4)). See the IRC Section 408(m) for the full definition of a collectible (the exception (3) only applies to Sec. 408 about IRA investment limitations, not Sec. 1 for tax rates).
You only pay the tax on gain when you sell the collectible, you don't pay any tax for just owning it.