Student discount: Depends on the place. Some will accept any ol' college ID, whereas some will require you to have an ISIC card. There've been some discussions on here as to whether they're worthwhile. I'm too old and long done with school for that, so I haven't really looked into it.
International calls: If you can find a card here that's a good deal and will allow you to call from overseas (just check the details on the package) then go for it. Sure, you may find better deals wherever you end up overseas, but who wants to spend that extra time running around looking for phone cards? As far as using them on any payphone - it really varies by country and location. In London, for example, I could ONLY use cards on some phones, and only coins on others. In Costa Rica, the phones would only take local calling cards, but there were other international phones (mostly in the hostels and internet cafes) that took foreign cards. Best bet is probably to get one with just enough minutes and a reasonable rate at home, and if you need to buy a local one, grab one. It shouldn't cost too much, wherever you are.