Has Taiwan been recognized by United Nations as an independent nation?

No, Taiwan has not been recognized by the United Nations as an independent nation. It did once during China's communist revolution in the 1950s-1960s. However, in 1971, China or "People's Republic of China" gained entry to the United Nations. Thus, "Republic of China" or Taiwan was expelled as a member. Taiwan has been trying to get membership into the United Nations, but since China is insistent that Taiwan is part of China and China is a permanent security council member, they've been vetoing Taiwan's bid for readmission.