​Sources

Fact or Fake 1: Fact.
Cleopatra VII was the last active ruler of the Ptolemaic dynasty, and she is noted as the first member of that dynasty to learn Egyptian.
Source: Encyclopaedia Britannica - Cleopatra Facts.

Fact or Fake 2: Fact.
Marble Arch was designed as the main entrance to Buckingham Palace and was moved to its current Hyde Park location when the palace was extended in 1851.
Source: Historic England - Marble Arch.

Fact or Fake 3: Fake.
The UK did launch its own rocket into orbit: Black Arrow placed the British Prospero satellite into orbit from Woomera, Australia, in 1971.
Source: GOV.UK - Black Arrow.

Fact or Fake 4: Fact.
Darwin had researched his species theory for more than twenty years, then Wallace's 1858 manuscript prompted the joint Linnean Society presentation and Darwin's later Origin.
Source: Darwin Correspondence Project - Origin.

Fact or Fake 5: Fake.
The beard-ban claim is not supported; the better-known Henry VIII beard-tax story is itself described as a legend with scant evidence and no National Archives record.
Source: Historic UK - Henry VIII's Beard Tax.