I actually think, as I think you point out as well, that privacy, if any, is going to be in short supply. What are they going to offer privacy for if a digital Euro is every controller's dream?
In any case, there will always be ways to escape. The ECB will know everything that anyone using the digital euro does but for illicit activities (or pure privacy of licit activities) other fiat currencies, gold and silver coins or cryptos will be used as in Sweden, where cash has practically disappeared.
Regarding the last question, it is not clear to me. I think that both the Yuan, the Dollar and the digital Euro are going to be launched at about the same time, although it seems that the Yuan will be the first, and, when it does, the US and Europe will not want to be left behind, so I don't think it will affect the exchange rate significantly.