When charging, the solar panel and the charger will safely charge the battery
the battery does not "need" current
it will provide the current the load requires, at 12V.
the energy contained in the battery when it is fully charged is (12V) * (2,4Amperre hours)
at 3600 seconds/hour, 8640 coulombs
at 12 volts, 103680 joules
that energy will come out of the battery to the load at whatever current the load requires
the fuse will protect the battery and the charger in case of a fault at the load
you specified a 1A load current
The circuit I expect to draw around 1A max
so a 2A fuse should be enough to allow operation and provide safety
the IN219 is intended for high side operation. your load is not high side
you can use a simpler device
your cable selection looks okay.
the 4mm is the diameter you specified in the first post
I use special cable (4mm) for DC current from solar panel to the solar charger...