mAh reflects how long they'll go (3000 mAh implies 3000mA for one hour). You can start playing around with the #s - like 1000mA for 3 hours, just be aware that it's not linear, meaning it won't work exactly as the math would suggest. I believe that you get less performance from high current draw situations.
If your wall wart puts out 700mA (no need to measure it) you can safely say the DAT will not draw more than that and very likely a fair bit less because the power supplies are always over spec'd for the application.
Voltage is always changing.
Alkalines start at 1.5 and work their way down over the life.
NiMh batteries fully charge at just over 1.4 and hold a pretty steady voltage until about 1.2 - once it starts to drop below 1.2 the end comes quickly. Note that this is one of the great features of NiMh - holding the voltage til the end.
NiCad batteries I'm not as familiar with. I think they charge to about 1.25 volts. I don't use NiCads since the NiMhs have come along.
I'm sure your DAT has an acceptable voltage range (in the manual or by experiment) that can work with a NiMh pack.
*wait* *googling*http://www.solorb.com/dat-heads/digests/V2.800/D851#Msg1Sounds like 6 - 9v is OK and current draw varies with voltage. You can do the math to figure out what batteries you need for a given run time. Only count on getting say, 80% of the rated capacity to be conservative.
Here - this guy did a NiMh pack with 5 cells (range 6-7 volts depending on charge state).
http://members.cox.net/barryklein/dat.htmWhen looking at RC packs, you really want NiMh, not NiCad. You generally get twice the capacity from the same size pack and as tapers, we usually need the extra juice.