Up to 128G. A 64G memory card is included in the package. 

Dear Customer, Thank you for your question. Please check the following steps to setting the focus: (Do not look at too close objects) Step 1. Cover the right objective lens with your hand or close your right eye, rotate the central independent focusing wheel until the image in the left eyepiece is sharp and clear. Step 2. Now cover the left objective lens or close your left eye, rotate the right eyepiece focusing wheel to adjust the diopter of the right eye until the captured image is sharp. 

Step 1: Being careful not to touch the lens, cover the right objective lens (or close your right eye) and turn the central focusing dial until the image seen by the left eye is clear. Step 2: Cover the left lens (or close the left eye) and this time instead of turning the central focusing wheel, turn the diopter adjustment ring (located near the right eyepiece and displayed on the small image in the upper right) until the image is clear. Step 3: Finally look through the binoculars with both eyes until the image is clear and sharp. 

Yes, as long as you are in close proximity to the camera 

The camea can take 1.6v rechargeable batteries, but in general rechargeable battery might drop its voltage quick depend on its physical performance. In the cold weather, recommend using Energize lithium batteries to get longer lifetime.