This info is within my limited knowledge.
So it is welcome anybody to point out where I may be wrong.
1. Phillipine's version: depends on if they have LTE or not. If not, it will be same as International version I believe.
2. No, it will not work in Canada. LTE band is a kind of mess, and it use different band and class depend on which country a unit is sold. Canada and US use same band, I belive Mexico is trying to get on same band right now.
3. International version should work with almost any carrier anywhere that use 2100Mhz for 3G and HSPA+ if available. In US, AT&T will work but no T-mo. T-mo use 1900Mhz I believe, you only can get 2G Edge signal (I found this a hard way yesterday. Unlocked att phone only gets 2G Edge:-[). Does anyone know International one has the band T-mo use as well?
I just find it out S3 international version has 850/900/1900/2100 capacity. So it will work on T-mo as well!