Did Adam and Eve REALLY exist?

Yes Adam and Eve really did exist. And we are bound to believe it since its a teaching proximate to Faith (sententia fidei proxima)

Its explained very clearly and concisely in Ott which I recommend all Catholics get a copy of (Ott, L. (1957). Fundamentals of Catholic dogma.)

"The whole human race stems from one single human pair. (Sent. certa.)

Against the Pre-Adamite Theory (first expounded by the Calvinist Isaac de la Peyrère, 1655), and the view of certain modern scientists, according to which the various races are derived from several separated stems (polygenism), the Church teaches that the first human beings, Adam and Eve, are the progenitors of the whole human race (monogenism). The teaching of the unity of the human race is not, indeed, a dogma, but it is a necessary pre-supposition of the dogma of Original Sin and Redemption. According to a decision of the Bible Commission, the unity of the human race is to be reckoned among those facts which affect the foundations of the Christian religion, and which, on this account, are to be understood in their literal, historical sense (D 2123). The Encyclical “Humani Generis” of Pius XII (1950) rejects polygenism on account of its incompatibility with the revealed doctrine of original sin. (D 3028)."

image from the 'Public domain' via wikimedia commons.  Adam and Eve  by Cranach, 1533