My realtor said no fridge or laundry machines because of liability issue, but throughout the years of renting myself I never had to bring in my own fridge and laundry machines.

I once moved their food to my fridge for a few days

That should have a limit that provides enough coverage to replace those items you own in the building that are not permanent (Stove, Fridge, etc.).  

I was thinking stainless steel ( fridge, stove, dishwasher and microwave) Thanks in advance.

Is a wine fridge a selling point in your area?

compare the actual savings between the two models.I recently bought a fridge (I know its not the same thing, but concept-wise) and looked into a regular one versus a efficiency one. 

I also have a fridge with a ice machine but no water line to hook it up.

From what I understand, we are covered for, what the insurance agent calls "vandalism and criminal mischief" from a tenant, with a 1000 dollar deductible.However, if the tenant steals anything, like the fridge or a/c, we have no recourse on the part of insurance coverage.Is it recommended to use the insurance or to just pay out of pocket?

Only the higher end homes have fridges with water/ice makers.  

Stainless Steel Fridge (Personal): Recently my fridge went out, and after a few diagnostic attempts, it was finally fully fixed on Friday.