You need to see a high quality estate tax lawyer. Your estate planning documents should provide that upon his death the assets are left in a qualified domestic trust for your benefit, which means that a U.S. person needs to be the trustee. That will avoid estate tax on his death. Whether you should consider becoming a citizen depends, among other factors, on the size of your estate. This is not something to decide based on an internet site. Sit down with a quality lawyer for a couple of hours. Spend the money to get good advice.
There is no simple answer to your questions without knowing ALL the relevant facts. For example, an attorney will need to know how you hold title to your assets, whether you have a trust, how that trust is structured, the value of your estate, etc...
Generally, a non-citizen can still inheret property in the USA, but the exemptions are much less than for citizens. If you have a lot of assets, I suggest you contact a estate planning attorney as soon as possible to have him/her analyze your particular situation.
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The answer to this question depends on many factors, including where the property you own is held - Canada or the US. You will want to speak with an estate/tax attorney in the US or Canada, wherever the property is located, to determine what is best from an estate planning perspective.