Spoiler alert- In the end of the game Booker is killed by versions of Elizabeth which would creat a paradox, but also it wouldn't solve the problem, since that wasn't Booker from the past that they killed, but Booker from the future in a dimension from the past.
The Animatronics are left on over night because they will take too long to fire up when turned on in the morning, yet leaving them on overnight a certain amount of times is bound to run out of power a