With regard to your questions, my amateurish efforts (almost all via the internet) are as follows:
Alexander Cobham was indeed born in Ballycarry, Broadisland (also known as Templecorran), in County Antrim in what is now Northern Ireland. The date of birth was (I believe) 24th March 1736 (source: Family Search.com).
His father was James Cobham (m. abt 1735; died 1797; buried in Templecorran church), whose father was the Rev. James Cobham, a famous Presbyterian minister. James Cobham junior was well to do and a wine merchant in Carrickfergus. His name appears in the list of Grand Jurors for the County of the Town of Carrickfergus in 1754, and also appears amongst the elected officers of the Carrickfergus Royalists Company of Volunteers in 1784.
He is referred to as a host of John Wesley when the latter visited Carrickfergus in May 1760.
James Cobham junior owned two houses outside the Irish Gate on the north side of the Irish Quarter, in one of which he may have resided. At a date, now impossible to determine, he removed to a house on the south side of West Street, where he resided in 1771 and probably until his death. He also owned other properties in Carrickfergus.
The Rev. James Cobham (1678 - 1759) was the Presbyterian Minister for over 50 years (from c. 1700) in Ballycarry (or Broadisland), County Antrim. This was the oldest Presbyterian church in Ireland, founded by Edward Brice in 1613.
The Rev. James Cobham’s father was the Rev. Thomas Cobham (d. 1706), who was Presbyterian minister of Dundonald and Holywood Presbyterian churches in Co. Down, from his ordination in 1678 to 1702 (or 1704), when the two churches were separated. He then continued at Holywood until he died in 1706. [Note that there was another Rev. Thomas Cobham, Presbyterian Minister at Clough in Co. Antrim, but in Proceedings of the Wesley Historical Society it is stated with some confidence that it was “Dundonald and Holywood” who was the father of the Rev James.]
Returning to Alexander Cobham, the records of the India Office show that he sailed to India in the ship Success in 1783 - 4 as a ‘free merchant’. The Gentleman's Magazine and Historical Review, Volume 79, Part 2 (Aug 1809) in reporting his death stated that he "acquired a handsome fortune in the service of the East India Company".
Until 1786 he was ‘Alexander Cobham of Binfield’ (Binfield is near to, but separate from Shinfield) ; in 1787 he married Charlotte Slade, was appointed by commission a Deputy Lieutenant of Berkshire and purchased the Shinfield Estate from his brother in law John Slade and the Earl of Fingal (possibly they were trustees); however, he pulled down the old Manor House and removed with his wife to Shinfield Grange. He served as High Sheriff of Berkshire in 1790.
The couple had no children, and Alexander made provision for leaving his money to his relations. He made a will in 1804. As was the fashion in the days of primogeniture, he wanted to leave everything to one relation (preferably male), to carry on the family dynasty, but if that heir died without male heirs, the property would pass to a different male heir of the testator. In the will in 1804 the estate was to go to his youngest nephew - the third son of Alexander’s sister Mary Craig (1750 - 1825) - called William (aged about 17 at the time). He was preferred over the eldest nephew, Edward (3 years older) who, it is speculated, had blotted his copybook whilst serving as a Lieutenant for the East India Company. Then, in 1806, William died and so Alexander changed the will to make the middle nephew (Thomas Craig) the primary heir, with Edward next in line if Thomas were to die without male issue. If both Thomas and Edward were to die without male issue, the estate was to go to the three Craig nieces, Mary, Sarah and Charlotte Craig, in a similar way. Only if none of the 6 were to have male issue was the estate to go to "cousin Catherine Martyr for life and her male issue successively". Catherine Martyr’s maiden name was Cobham, and she was the only child and daughter of Dr. Thomas Cobham (of whom more, below).
After 1806 and before 1809 the heir Thomas died. However, Alexander Cobham did not get round to changing the will again to accommodate this fact.
By 1808 Catherine Martyr had 5 living children, the youngest of which was a boy born in 1808; he was named “Alexander Cobham Martyr” in honour of his elderly relation, who was asked to be godfather to the boy. Relations between Alexander Cobham and the Martyrs became rather close … [to be continued ...]