I believe MaoMao is 17 when the story starts? But time actually progresses in this manga, so she would be older by now. I think she's a year younger than Jinshi? which would make her 18 atm I guess. Though at this point the manga and the webnovel is starting to become quite different, so i might be mixing information here.
As for the relation between Jinshi and the emperor, I don't believe it's been made clear yet? neither in the manga nor the webnovel i think. His official status is the emperor's younger brother, but a potential father-son relationship has been hinted at several times, so i guess it's still up in the air
Jinshi is another identity that the emperor's brother has. However, it is strongly hinted that Jinshi is actually the emperor's son. (chapter 18, page 20-24)
His mother was afraid that her son would be assassinated or that another situation would arise where doctor's wouldn't prioritize her or her child like they did when she was to give birth. She swapped her mother-in-law's child with her own. So when Jinshi is thinking "if her son was still alive today..." he's actually thinking of himself without knowing it http://www.mangago.zone/read-manga/kusuriya_no_hitorigoto/nbt/mpn_chapter-2297913/pg-17/
Soo if Jinshi is 19 how old is MaoMao