Actually how can Mexico even afford the nukes?
The same way that North Korea and Pakistan can OTL... If you think they're important enough, you'll make your people eat grass to get them.
I'm surprised by how's few nukes there are. The fact it took until 98 for the US to get any and the fact they let Mexico have any. Especially since that last one feels like it would be a trigger for another Mexican-American war.
Before Mexico announced its nuclear programme, there wasn't considered any particular need for the US to have a nuclear deterrent, seeing as she's not a very active country militarily TTL. There was a bit of public clamour after Mexico unveiled its first weapon, hence the decision to pursue an American deterrent. At first, the idea was that this deterrent would be 'American Made' before the program was eventually completed in cooperation with Sweden and Britain.
As for whether it would start a war: why would America attack Mexico now? They have nukes.
On the question of amount, there are a couple of things to say. Firstly, bear in mind that the numbers are deliberately stated to be lower bound estimates so the actual number of nuclear bombs lying around TTL is probably higher. And secondly, the idea is that a number of missile reduction programmes brokered by Brazil and other non-nuclear powers brings down the overall number during the 21st century.