the 1000 mA is what the power block can provide. It does not have to. This is “controlled” by the Photon - it just consumes what it needs. There is only a problem if the power block cannot provide enough current. There is none if it can provide “too much”.
There could theoretically be a problem if the voltage would rise up in case “not enough” current is consumed, but that is not the case for a battery and in any case the voltage regulator of the Photon should be able to deal with a wide range of voltages. So don’t worry!
The how long question sounds like simple math, so it should be slightly less than 9 hours. But in practice it will be less. But this highly depends on the power block and how close to the claims they make they are. So I would say it is certainly less than 9 hours, but how much can only be found by experimentation. Anything between 2 to 7 hours sounds realistic for me. If it is a cheap one then it is probably closer to the 2 hours…
But the question is also if the 250 mA figure is what you want for a battery powered application. I have an application were the photon runs for months with a 400 mA battery. But it is almost always in sleep mode and only wakes up on external events and only enables the WiFI in certain events. Is your application really needing the WiFi and the full processor all the time or can it sleep for times? And I even don’t think that with WiFi it really needs the 250 mA all the time. I would have to double-check that, but I think if you are not actively sending or receiving data it is in practice less.
Hope that helps!