How did the women cope on the First Fleet?

Answer 1

Badly.

Conditions were very unsanitary, and dysentery and cholera were common, though less common than on subsequent fleets. Women had no privacy, and there was no provision for bathing. Basic personal hygiene was something that simply could not be attended to.

The convicts, both male and female, shared ship space with rats. Men and women were given small rations of basic flour and salted meat. Occasionally they were permitted to walk around the decks for exercise. Women were often used by the marines for their "entertainment". As food was sometimes in short supply, many of these women willingly traded their services for extra rations.