A:AnswerI'm not sure what you mean by anti-shake but if you're referring to image stabilization on video, it is not that great. It is called Digital IS and has three options: Off, On, and Enhanced. It does its best but you may have to use software during post to stabilize your footage.
A:Answerit has F2.8 but playing with it, you can get better results with a DSLR and a lens with F2.8. An iPhone and higher end Android phone may do a better job with background blur.
A:AnswerYou can’t zoom the camera itself. However, on the iPhone I can pinch the image and zoom in on a specific site I am interested in without loosing resolution.