Electrical – Should all the home’s GFCI outlets be connected to a GFCI breaker

If the lights stay on while the breaker is tripped, they must be getting power from another circuit. That means the electrician has mixed wiring between two different circuits. A GFCI breaker trips if there's any imbalance between the hot and neutral wires connected to it; if the lights are sharing the GFCI circuit's neutral wire while also drawing some power from a different circuit's hot, the breaker should definitely trip. The arcing you mention further reinforces that the wiring for the lights has used a hot from a different circuit while using the GFCI's neutral.

What you need to do now is figure out what the second circuit powering the lights is, figure out where it's tied in to the lights, and either disconnect it from the lights, or make sure the lights only use the neutral for that circuit.

You can run the fridge but not the dishwasher as shown in exhibit 210.28. It also depends on where you live local code may have exemptions or tougher requirements. I usually run a dedicated circuit for the fridge. There is an exception that allows a gas stove igniter and a clock outlet on the 2 small appliance circuit. The wording is counter top a dishwasher, Garbage disposal, trash compactor and in some cases a built in microwave require additional circuits. It really depends on local requirements. But Exhibit 210.28 clearly shows the fridge not gfci protected and on 1 of the 2 small appliance circuits. (The Exhibit is 2 drawings of methods that can be used for the required 2ea 20 Amp small appliance circuits in the 2014 NEC hand book).