1. It is an obligation you eventually have to settle. There is no guaranteed way to succeed.
(Some people may use their U.S. Passports as a cover. But again - the Passport will show the person is born in Taiwan.)
2. A newborn child of a U.S. citizen is a U.S. citizen automatically. Simply follow here to complete the process:
http://acs.ait.org.tw/report-birth-abroad.html
As a native-born citizen, the newborn is not eligible for a U.S. visa as a matter of law.