Requirements 2,3,4 you'll comfortably get in a decent double din head-unit with sat nav and a reverse cam input (plus obviously the camera), I can't recall seeing one that will do number 1 as well though.
I've got a cheapo innovv cam for front facing recording http://www.innovv.com/#!the-c1--c2/c13dx
I've not got round to wiring it in permanently, so I use it on demand, but with a live off the ignition and a decent sized memory card it can be configured to switch on and auto record on power up and it loop records on the memory card in 10 minute segments, so all you have to in the event of accident is get the memory card out before it loops back and records over itself (several hours).