K&F Concept-301 16MP 1080P HD Trail Camera 0.4s Trigger Outdoor Waterproof Hunting Infrared Night Vision Mini Camera, 2PCS

SKU: KF35.006V2

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No. The manual says "Regular SD memory card (max capacity 128GB, Class 6 or above) If you can't find a 32gb, I would say go with a smaller GB class 10. 
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Yes it does. During the night vision mode, there is a small Red light that activates when the motion sensors are activated. 
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On the camera, there is a viewing field, so yes, you can. However, there is no sound 
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Yes, I believe you can with any trail cam. There are several videos on YouTube. You need a 4.0x1.7mm plug. I saw one video that explains a direct hard wire. After watching some videos, I decided it was easier and about the same price to buy the Stealth Cam 12v external battery pack with solar panel. I paid $50 at Academy Sports online. Plus the 4.0x1.7mm plug from Amazon. But if you like to make things, there are plenty of videos on making your own solar battery packs. 
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Yes. It has a 12v external jack. I found that if you run the camera with just a solar battery pack, you have to unplug it every time you open it to check the memory card. When you do that, the date and time reset. Leaving batteries in the camera solves this problem. 
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It takes good photos/videos in all lighting conditions with its fixed focus lens 
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I pull the card and put it into a card reader on the computer for easier and better viewing 
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Yes. Go to the menu and pick the mode you want...picture, video or picture and video.