No, you don't need to separately depreciate all "improvements" (remodeling, furnace, roof, etc.). Those can be all lumped together because they were all part of the house when it was "placed in service".
However, you CAN (and should) separately depreciate non-building improvements, such as appliances. You would usually use the Fair Market Value when you converted it to a rental. Those are depreciated separately because they are depreciated differently than the building itself.
In answer to your question, NO, you don't "have" to use that ratio of building to land. That is just a make shift provision. You are right that using the current ratio (after making improvements) is likely to change the real number that should be used.
Assuming the valuation has increased since you bought the property, you should use the amount that you actually PAID for the land when you bought it. Because that is rarely known, the using the ratio of building to land value when it was purchased is usually the easiest way to do it, but you can use any reasonable other method to come up with determining what you paid for the land.
