Ruby's mentions of stepping on a butterfly and the butterfly, which the doctor then revives, are a clear reference to Ray Bradbury's short story "A Sound of Thunder" in which a time traveler travels into the past and, by stepping on a butterfly, changes the future and when he returns to the present, the changes were terrifying. The story was published in 1953 in the book The Golden Apples of the Sun.
The Doctor alters Ruby's mobile phone so she can ring her Mum. The Ninth Doctor does the same thing for Rose in 'The End Of The World'.
The situation with the babies is a not so subtle jab at anti-abortion groups; not caring about the babies beyond them being born. Ruby even acknowledges the bizarre similarities.
The Doctor repeatedly corrects himself when he mentions the babies to say 'space babies' - the 12th Doctor censured Clara for putting 'space' in front of words (in Clara's case, 'Space Restaurant'). Clara retorted by calling The 12th Doctor a Pedant - which is one of the titles the 15th Doctor says is used by the Time Lords.
The fact the Doctor gives Ruby an Abridged version of his backstory off the bat shows how much the Fourteenth healed. Up till that Doctor, he had been very guarded and secretive since the Time War.