Is the self-powered USB hub powering my devices?
The simplest way to know if your hub is providing power to the ports or not is to just plug something into it while it's not connected to the computer. If it gets power then the only place it can possibly be getting it from is the hub's power supply.

How much current it can deliver depends very much on how they have designed the hub. Many cheap hubs just have a direct connection between the power supply and the power pins of the ports. The only limit then is what the power supply can provide (less what the hub itself needs to operate). 

Better ones include power control and over-current sensing, etc. In these cases, if they are to adhere to the USB 2.0 specs, then 500mA is the minimum current they should be able to provide whilst self-powered, or 100mA when bus powered. Any more than that and, at the hub's discretion, the power may be shut off.

Of course, the hub is free to provide considerably more current, in which case it can be classed as a CDP - Charging Downstream Port - which can be used to charge high capacity battery systems like mobile phones, etc, where they request (or expect) much higher currents than the USB 2.0 spec allows for a standard port. 

So the only real way of knowing just what your hub can do is to pull it apart and see what kind of power circuitry is connected to the power pins on the ports, and look at the datasheets for any chips involved.