Yes. 

No, not support. 

Yes there is a case/stuff sack and as far as accessories there are two batteries, charger, and 32GB MicroSD card. Pretty sure there was a lens cloth as well. 

Dear customer: This construction time-lapse camera is a waterproof and dustproof integrated design, and the rating is IP66, so you don't need to protect items such as cases. Hope our answer is helpful to you. 

The maximum aperture of an ultra-wide-angle lens below 24mm will have a slight cross shadow in the 1-5 gear dimming. The longer the focal length used, the smaller the effect of the cross shadow. There will be obvious cross shadows and vignetting in the large gear of dimming. If you continue to rotate the shadows, the shadows will disappear naturally, which is a physical phenomenon and not a product problem.