Let's say Valerie is a French citizen living in France. She has assets in the state of California that she wishes to pass to her niece, Carol, who presently lives in Oregon. One option Valerie has is making a will that conforms to the laws of California in which she directs those assets go to Carol. But there are other ways to pass those assets, too, that avoid probate altogether. As others have mentioned, if the assets are financial accounts, Valerie could simply name Carol as her pay on death (POD) beneficiary of the accounts. She'd do that with the institution that holds the accounts. Then when Valerie dies Carol automatically becomes the owner of those accounts. Another possibility is creating a trust and putting those assets into the trust. Then when Valerie dies the trustee of the trust follows the directions in the trust document as to how the trust is to be distributed.
However, because Valerie is not a citizen or resident of the US for tax purposes, if the assets she had at the time of death that are considered to be located in the U.S. exceeds $60,000, the U.S. will impose a hefty estate tax on the amount over $60,000 that will take a pretty big bite out of those funds. The unified credit against federal estate and gift tax is vastly smaller for nonresident aliens (NRA) than it is for citizens and residents of the U.S. Note that the rules for which assets are treated as located within the U.S. aren't entirely intuitive. For example, bank accounts held by a NRA in U.S. banks are not considered to be assets within the U.S., a rule that was adopted to aid the U.S. banking industry in attracting foreign deposits. But other types of financial accounts in the U.S. may be sourced to the U.S. and subject to the tax. For example, shares of stock of a corporation organized in the U.S. will be treated as located in the US and will count towards the tax.
My point here is that if you are a NRA and the assets you have in the U.S. exceed $60,000 in value you may want to consult a U.S. tax attorney to ensure that the assets you have won't get hit by the federal estate tax. You can adjust your assets to types of property that are not taxed to avoid this problem if necessary.
That's not correct. Your will does not become invalid just because you become a nonresident of that state. What might happen is that the will you did in the first state might not meet the requirements for a will in the second state. In which case your assets in that second state would end up distributed by the intestate succession rules of that second state unless you did something to ensure they pass outside probate (like designating POD beneficiaries or using a trust). Most states have similar requirements for a will, so in a lot of cases there is no need to redo a will just because you move from one state to another. But you do always want to check to be sure.
No. But it does matter in what state(s) the assets are located.