1. When can the normal distribution be used instead of the binomial?

When the value of n, the number of trials, is large and the value of p 
(the probability of a success at each trial) is close to 0.5.

2. Is there any easy way to test whether the normal can be used to approximate to the binomial?

If nq ≥ 5 and nq ≥ 5 then the normal can be used.
(remember that q = 1 − p)