Short answers, pulled from the story.
Domicile in law is the legal connection between an individual and a specific jurisdiction that governs their personal law, including rules on status and property. It is independent of nationality: a person can hold United States citizenship while being domiciled in Kentucky, or hold dual nationality while still having only one domicile at a time.
Domicile of origin is established by law at birth and is based on the domicile of the relevant parent, not necessarily the place where the child was born. In the case of Udny v Udny, a child born and raised in Tuscany was found to have a domicile of origin in Scotland because his father's domicile of origin was Scottish.
Acquiring a domicile of choice requires both actual residence in the new place and a genuine intention to remain there permanently. Canadian case law defines this as making that place one's principal residence indefinitely, and the ability to settle permanently has been held to arise only when a person can become a permanent resident for immigration purposes.
The Alberta Court of Appeal in Foote v Foote Estate held that Eldon Douglas Foote, who died in 2004, remained domiciled on Norfolk Island despite purchasing a condominium in Victoria, British Columbia, because his plans to relocate permanently were undeveloped and his intention was ambiguous. The court noted that abandoning a domicile of choice requires both the cessation of intent to reside permanently and actual acts ending residence, and these two conditions must be met simultaneously.
Under section 267(1)(b) of the Inheritance Tax Act 1984, a person not actually domiciled in the UK is treated as UK-domiciled for tax purposes if they were resident in the UK for at least fifteen of the twenty tax years immediately preceding the relevant tax year and for at least one of the four tax years ending with that year. A separate three-year rule extends deemed domicile for three years after a person who was actually UK-domiciled changes their domicile.
Nine US states, including Florida, Texas, Nevada, and Wyoming, levy no state income tax, so establishing domicile there eliminates state income tax on worldwide income regardless of where that income is earned. Florida additionally offers unlimited homestead protection against creditors for a domiciliary's primary residence, and Florida, Texas, and South Dakota impose no estate tax. The source notes that over half of contested domicile claims result in adverse findings for the taxpayer when high-tax states audit former residents.