Also, its pretty standard around my neck of the woods to provide a fridge. 

I promise a $100 electric bill for the month it takes to evict is cheaper than a new fridge (destroyed by mold), new paint (used candles), pipe break restoration (no heat in winter), or any other the other many issues that could arise.

Under this rule can I deduct the purchase of a new fridge, washer dryer, microwave, dishwasher for a rental property bought in 2016, all under 2500 with bills for each?

Ten times the houses means ten times the roofs, ten times the furnaces, ten times the fridges, etc.

I put about $2k into the property for painting, cleaning, landscaping, fridge, etc...)  

I still never offer fridges with water dispensers or icemakers.  

If space is that tight, as J Scott said, use an over the fridge / stove style, you could still put lighting on it to shine on sink.

Before she left she actually told me I should throw away the fridge, it was too dirty to clean.

But they are pulling a New York attitude about the whole thing, saying we lost tons of food when the fridge didn't wasn't cooling properly for a week. even though my asst. gave them a small fridge temporarily. 

I state in my lease that the fridge and stove are included appliances.