To answer your second question first -- "Is it realistic they'd not know how far away, to the west, Asia is?" -- I would say, Yes. Christopher Columbus, before setting sail for the "Indies" (India, China, Japan), studied many of the then-preeminent works of geography and natural history: the travels of Marco Polo (who had visited the Yuan in China) and John Manderville, Pliny's "Natural History", the "Historia Rerum Ubique" Gestarum of Pius II, among others. We know this because he took detailed notes on these books. And from these book, he came to the mistaken conclusion that the eastern coast of Asia was much nearer Europe than the reality; in fact, that Spain was nearer China heading west, over sea, than heading east, over land.

To partially answer the first -- "Is it realistic that the English would be unaware that the Yuan no longer control China?" -- Columbus himself did not know this. In his notes on Marco Polo, he focused on descriptions of the court of Kublai Khan, in hopes of preparing himself for a meeting with one of the Khan's descendants. In fact, he carried a letter from the Spanish Monarchs addressed "To the great Khan."

Here is an interview with a professor at Stanford, discussing how a primary motivation for Christopher Columbus was to attempt to convert the Great Khan of China and hopefully convince him to join Spain in a Crusade against the Muslims in the Holy Land.

And a quote from "Genghis Khan and the Making of the Modern World (Weatherford, 2005):

“With so many empires striving to maintain the illusion of the Mongol Empire in everything from politics to art, public opinion seemed obstinately unwilling to believe that it no longer existed. Nowhere was the belief in the empire longer lasting or more important than in Europe, where, in 1492, more than a century after the last khan ruled over China, Christopher Columbus convinced the monarchs Isabella and Ferdinand that he could reestablish sea contact and revive the lost commerce with the Mongol court of the Great Khan. With the breakup of the Mongol communication system, the Europeans had not heard about the fall of the empire and the overthrow of the Great Khan. Columbus, therefore, insisted that although the Muslims barred the land route from Europe to the Mongol court, he could sail west from Europe across the World Ocean and arrive in the land described by Marco Polo.”

Now, did the English know this? I cannot say. I speculate that they didn't, but have no proof. Perhaps another might..?

The Atlantis series by Turtledove?