On splitting of the conjugacy classes of $S_n$.

Question

I was reading this discussion to know whether a conjugacy class of $S_n$ splits or not when we go down to $A_n$. With this in mind when I read this wiki, I am confused when looking at the table called "particular cases". Indeed if we consider the second row i.e. we consider a permutation with decomposition 1+1+1 then we have 3 1-cycles so according to the criterion it should not split (since there are 2 cycles of same length). Also I was wondering why when the class splits, it splits only in two classes and not 3,4,5,... And why if it splits in 2 classes the respective classes cardinality is divided by 2 (it could be that more elements of the original conjugacy class go into one of the splitting class than the other no?).