How are vacation rental losses treated post sale?

We're looking at doing a 1031 or sale of our vacation home in the next couple years. 

 

Let's say if we bought the house for $500K, improvements of $100K, depreciation of $50K, would my property basis be $550K?

 

1) If I sell for $600K, that means a gain of $50K?

 

2) If I sell for $575, that means I have a passive loss of $25K? 

 

Is that a correct assumption of how costs would work out given above assumptions?

 

Also in scenario 2, as I'm not a real estate professional, do I have to continue to carry over the $25K loss until whenever I sell my primary house for instance to be able to use that $25K loss? Basically carry it over indefinitely if I don't ever buy another property?