Tell us about yourself!
An xbox360 PSU is unable to supply 1000watts (a fifth of that, at most, and that would already be out of spec), luckily your amp probably doesn't come close to that output either, so it probably is fine. I'd suggest to have an eye on the PSU anyways.If you want to know your real output (and even efficiency and with that, input necessity) of your amp, I suggest having a look at http://amp-performance.de/106-von-Alpine-bis-Zapco... then pick the manufacturer and model. If it happens to not have been measured yet, pick a model close to your rating and look at the real numbers. If the amp actually draws anywhere close to the 1kW (I reckon it's about 200W RMS at most), be extra careful with using the xbox360 PSU, as it's weak. Very weak.
The connection would be in parallel, voltage only adds up if connected in series. Connecting a battery in parallel to save settings is absolutely possible.