The binomial distribution can be approximated with a normal distribution when np > 5 and np(1-p) > 5 where p is the proportion (probability) of success of an event and n is the total number of independent trials.
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There is no such thing. The Normal (or Gaussian) and Binomial are two distributions.
Use the continuity correction when using the normal distribution to approximate a binomial distribution to take into account the binomial is a discrete distribution and the normal distribution is continuous.
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The binomial distribution is a discrete probability distribution which describes the number of successes in a sequence of draws from a finite population, with replacement. The hypergeometric distribution is similar except that it deals with draws without replacement. For sufficiently large populations the Normal distribution is a good approximation for both.
As n increases, the distribution becomes more normal per the central limit theorem.