...Typical battery life for alkaline AAA in ActiveEye?...
I can't remember when I put mine in it's been so long.
...Can I use NiMH rechargables?...
I don't recommend NiMH batteries (or NiCd ones for that matter) for this application. Most rechargeables will lose stored power faster than the small drain of the ActiveEye. "Precharged" NiMH batteries such as the Endloop brand are the exception.
The real problem comes with the battery voltage. Alkaline batteries have a typical per cell voltage of 1.5V while MiMH and NiCd ones are 1.2V.
Someone posted a while back that the specifications for the components in the ActiveEye say their minimum voltage should be 2.5V.
* This means that while a pair of alkaline batteries providing 3V will be acceptable, a pair of NiMH ones will only providing 2.4V won't. Also if you have cold winters, you need to factor in that can lower you output also.
Bottom line: While I go green and use rechargeables whenever I can, this is not a good application for them.
*http://forums.x10.com/index.php?topic=36.msg82408#msg82408Wow it took a while to find that post. - Read above and following posts.