Understanding Battery Controller
Yes
Yes
Yes, plus the maximum current sent to charge the batteries is also 5 A.
The charger will cut out charging at 14.6V to avoid overcharging the battery, and...
... Will start up again once the battery voltage has dropped back to 14.0 V
Will disconnect the load if the battery goes above this (in case someone's done something stupid and is trying to feed power back in to the controller's output)
Will disconnect the load if battery voltage goes below this (to prevent the battery being completely discharged)...
...and will reconnect again once it rises above this value
Copy of 6.
Not sure.
My guess is that it only turns on the output when the solar voltage drops below this - presumably so that lights are turned on when it gets dark.
Two different types of lead-acid battery.  "gel" are safer because the acid electrolyte doesn't spill if the battery is dropped/knocked over.
Max voltage of solar panels.  Going over this is liable to damage the controller.
Max voltage of batteries.  Going over this is liable to damage the controller.