Question: why did yomo take rize?
Answer: I think that her body has been revitalised after being turned into a Nucleus/Dragon/whatever. Yomo handed Rize over to Shachi who then eventually was killed by Arima so Furuta probably got his hands on Rize around that time. ... Dragon Rize is in the 19th ward, while Kaneki's Dragon was only in the 1st, 4th and 13th wards.