1) it will run on the CDMA but not LTE (yet) -- it is "rumored" to be coming soon, but hasn't dropped yet.
2) The phone will work on any GSM carrier (AT&T, T-Mobile, etc.) even though ST will tell you it won't. Keep in mind though that the Verizon iPhone 5 (that ST is selling) doesn't have the right bands to get LTE on T-Mobile or AT&T (you will get HSPA+ but can't get LTE on it).
Hope that helps.