eeeeh, "enjoyment / benefit" is sometimes true but not always.
Sometimes in a relationship both parties agree that it is best if one party (usually the mother) puts aside her career in pursuit of raising the children. This party is at a disadvantage after a divorce, and in some cases it may be reasonable to compensate for it.
Ideally this should be a tiered system when payments wind down over time (but usually isn't).
It could be that her ex-husband made so little that the added money wasn't relevant, and the author chose not to bring him into it. That seems reasonable to me.
The duration of alimony is probably very dependent on the state. One example that I am aware of is that alimony is typically paid for half the duration of the marriage. If his new wife is beyond that period, then she may only be receiving child support.
You mean "child support".
Alimony is a payment directly to the ex-spouse, for the ex-spouse's enjoyment / benefit.