The babies are strapped into their chairs but the Doctor & Ruby pick them up without releasing the straps.
When Ruby leaves the babies to go to Portal 357 she grabs her jacket but immediately afterwards she's wearing it. She is never seen putting it on.
The Doctor mentions that he was a left alone in the middle of outer space and was taken in by the Time Lords. In the Timeless Child story arc, the Doctor is a foundling adopted by Tecteun, who was Shobogan, a species native to Gallifrey before the advent of time travel on the planet and before the rise of the Time Lords.