Does The Canon Rebel T3i Have Video Auto-Focus?

1. Does the Canon Rebel T3i have video auto focus?
2. Which is better T3i or T4i?
3. What is the best DSLR camera for beginners?
4. What brand is better Canon or Nikon?
5.Is it better to buy the BODY or the BODY & LENS together when buying the camera?

Read the manual:
http://gdlp01.c-wss.com/gds/0/0300004720/02/eosrt3i-eos600d-im2-c-en.pdf
Pages 151, 163: Overheating when capturing video.
Page 151: File size limitation
Page 151: video record length limitation (unless the camera overheats and shuts down, first.)
Page 152: Autofocus difficulties with video.
For video, the two still image capture devices you list are the same.
For video, using a dSLR is a poor choice because it is not designed to capture video. It is designed to capture still images. Video capture is a secondary convenience feature. Plan on investing in mics and XLR adapter.
Both companies make fine digital still image capture devices. Canon makes fine camcorders.
For still images, there can be "kits" that provide good deals - the point of an interchangeable lens system is to have many lenses - not just one.

This does not mean dSLR can't capture good video - they can. But you are asking questions that indicate you have little experience. Refer to page 163 about the built-in mic recording audio noise from the zoom and auto-focus motors. The resolution is to use an external mic. Think about how you expect to mount this (use a camera bracket).

There's LOTS more, but if you think you're getting in inexpensively to video, you are in for a big surprise. As a beginner, you are better off getting a camcorder and learning before jumping into using a dSLR for video.

If a dSLR footprint is required save your money and get a Black Magic Designs cinema cam or Canon EOS cinema cam. The dSLR specifically for video will be painful. Use the dSLR for still images.