A secondary fuse in that design primarily protects the rectifier/diode. The car battery won't care much, you can dump 20 amps into a car battery for hours without hurting it much.
The heat produced in the rectifier is determined almost entirely by current, the 6/12 volt setting won't change that, so select the fuse to protect the most expensive part, the diode. (The amp rating for the charger is likely for either setting, as the reset/circuit breaker is set for that trip current)
Guessing a bit, but the transformer looks like it's good for several amps, as long as it has a primary fuse it will be ok. (if it doesn't, a 1/2 amp fuse to protect it may be a good idea, unprotected transformers start fires)) (Why this size is sorta complicated, theory would say smaller, but it will nuisence pop the fuse if the fuse isn't big enough to handle the inrush current when you plug it in. So, you go slightly bigger in this case, the short circuit current if the transformer fails will be much more than 1/2 amp))
As an aside, the rating is kinda funny, 4 amps at 117 volts is over 400 watts, but 1 amp at 12 volts is only 12 watts....are they implying this thing is that inefficient? LOL
