Most policies have coverage when an incident is "sudden & accidental". So the loss of power was sudden and accidental as such the fridge might be covered. Same rule applies for the water spots -- they didn't happen 'suddenly' or 'accidentally' so your coverage probably won't apply. Best of luck with making the CG own up to the damages of either - ideally they can't be held responsible for a high mineral content in the water.
Ask for a copy of your policy -- make sure you get the actual policy and not just the dec page-- and read the portion on Comprehensive coverage. It isn't in Latin and most are written pretty clearly. Pay attention to "excluded losses". Here's an interesting fact, dang few adjusters are familiar with the policy language. They all know the coverage for losses that occur every day but this one is rare. If you read the policy first and see the "sudden & accidental" verbiage and it isn't directly excluded in the excluded losses section you can win the argument by knowing more than the agent or the adjuster.
It doesn't cost you anything to open a claim. If coverage is provided, your Comp deductible applies. If coverage isn't provided you don't run the risk of having a claim and your rates go up.