Short answers, pulled from the story.
Middlesex was abolished on the 1st of April 1965, when the London Government Act 1963 came into force. The act dissolved both the administrative county of Middlesex and the administrative County of London, folding nearly all of Middlesex into the new Greater London.
Middlesex means "territory of the Middle Saxons." The name fuses the Old English middel with Seaxe, the Saxons' own name for themselves, which likely derived from the seax, a short notched knife they were known for carrying. The name was first recorded in Latin in 704 in a chronicle about a land grant at Twickenham.
Middlesex County Council met at the Middlesex Guildhall in Westminster. In a well-known administrative oddity, that building sat within the County of London rather than within the council's own area of jurisdiction.
The phrase originates at the Battle of Albuera in 1811, during the Peninsular War. Lieutenant-Colonel William Inglis of the 57th (West Middlesex) Regiment, wounded in the fighting, refused to leave the field and urged his men with the words "Die hard 57th, die hard!" The regiment held, and the phrase entered common English use. Middlesex Day, celebrated on the 16th of May, commemorates this action.
The wood anemone is the county flower of Middlesex, chosen by a public vote during Plantlife's 2002 county flowers campaign. The flower was historically common across the Forest of Middlesex and still blooms in woodlands that were bypassed when London's suburbs expanded over the county.
In April 1965, the outer London boroughs of Barnet (in part), Brent, Ealing, Enfield, Haringey, Harrow, Hillingdon, Hounslow, and Richmond upon Thames (in part) were formed from the former county of Middlesex. Seven inner London boroughs, including Camden, Hackney, Hammersmith, Islington, Kensington and Chelsea, Tower Hamlets, and the City of Westminster, were formed from the Middlesex territory that had been part of the County of London since 1889.