does the iPhone 4s have 4g capabilities

It depends on the definition of "4G". By International standards, there are no carriers anywhere in the world that have true 4G networks. But marketing departments don't care about technical standards. Verizon, for example, calls their LTE network "4G", and it is pretty fast; about 7-10 Mbps. AT&T calls their HSPA+ "4G"; it is really just a faster GSM, about 4.5 Mbps. Sprint calls their WiMax network "4G"; it is the fastest, at 15 Mbps, but it is only available in a limited number of locations, and outside of those locations they are way back at EVDO speeds of 1.5 Mbps.

The iPhone 4S supports HSPA+ on AT&T and other carriers, but not Verizon's LTE or Sprint's WiMax. So on Verizon or Sprint you are limited to EVDO speeds.

At at&t they claim they have 4g, but it's not LTE, it's just HSPA+, which is a slower 4g

Yes on T-Mobile..

No it does not, because an iPhone 4s does not have the built in hard ware to be able to use 4G. This is why Apple launched the iPhone 5, which does have this necessary hardware.

If you want 4G on your phone, then you'll have to upgrade to an iPhone 5. You cannot get it on an iPhone 4s.