a) Was the Great Famine real?

It was.

b) If so, was it as bad as we’re taught in the west

It was pretty bad, nothing like the fudged numbers of 60-80 million people dying, but 20-30 million are rumoured to have perish in that tragedy.

c) Was it directly linked to Mao’s Great Leap Forward

It was, but you must ask yourself why the great leap forward happened in the first place. Right after the Khrushchev got elected, the revisionist Soviets recalled industrial experts and scientists, effectively stopping its supplying or aiding of China's industrial efforts, it was effectively an embargo on China, this completely crippled China's momentum and forced Mao to take a radical approach of self-sufficiency to industrialize China in a way it can compete with other industrial nations.

The failure of the great leap forward was due to being a desperate plan rather than well-thought out one (that being said, many benefits actually did come from the GLF, such as literacy rates improved and living conditions were developed, so it wasn't a complete failure), after the great leap forward came the Ultra Poverty-worshipping communists such as the gang of five, who stated all that China needed to do was stay the course, and China would find itself a developed-industrialized nation in no time.

Had Khrushchev and the Bukharinite faction not took over after Stalin's death, the Chinese wouldn't have to be forced into such desperate measures such as the great leap forward, nor would the sino-soviet split even have happened. It's another reason why Mao had Nixon come over to china in the 1970s, it was desperation, and China needed its productive forces to be sufficiently developed, it needed foreign technology to accomplish this.