Take note that it is MOE that you'll be trying to convince, not NIE. For the teaching route, you would need to pass an interview and get hired by MOE, who will then sponsor you through NIE. I believe now they send you for at least one year of contract teaching before the school approves you to head to NIE.

1) Overseas uni accepted too. There's probably a list of "reputable courses", but I've no idea what it is. If you know of fellow alumni in MOE then you're safe.
2) 30 is fine.
3) I believe MOE is not trying to grow numbers right now so they're just recruiting to replace attrition. So rather competitive right now.
4) I'm not too sure, though since it's a relatively low candidature I suspect it's not that in demand. Would maths be something you would consider teaching, too? I know the MOE website lists what degrees they're looking for to teach various subjects; you should take a look there.