The battery to controller should be fused (unless they are right next to each other) as the battery can provide almost unlimited current on these wires. The panels to the controller does not need to be fused as the panel can only provide limited current which is always going to be less than the fuse rating anyway. Some folk use a circuit breaker between the panels and controller, but this serves as a switch as opposed to a current limiting device.
This is correct. I put a fuse between the battery and controller, and you don't really need one between the panel and controller, but I put one in there anyway. I prevent an arc when I unplug the solar panel from the controller with cardboard or something over the panel to block the sun, and then pull that fuse that I put between the solar panel and the controller. Or, you can use a circuit breaker, if you have one:)
BTW - It is rather surprising how much of a shock you can get from a 110W solar panel plug end.