Spec'ing power supply to replace a battery pack in a DIY project?
Measure it. If you already have the device you want to know about, wire an ammeter in series with the existing batteries and find out the peak current needed.

Most multimeters have an inbuilt ammeter.

Here's a good guide.

Yes, the amperage rating of a power supply is the maximum current it can safely supply for the given voltage. Over-speccing your power supply should not cause a problem so long as you don't short it.