Depreciation of rental property questions

[Ajay Kapoor]

I am purchasing my first rental property which is 20 years old for 300K. I wanted to understand how depreciation work in this case. since depreciation is allowed for 27.5 years. Since it was a primary home of seller, he never took any depreciation. After I purchase - 

1. will I be able to take depreciation for remaining 7.5 years or or also take back dated 20 years depreciation (since previous owner never took)? 

2. What will be the cost bases for me to calculate depreciation? 

3. What will be the formula to calculate depreciation (in either of applicable cases)?

4. Since I am in really high AGI tax bracket will depreciation be even allowed? I cannot deduct lot of other expenses as they are below certain %age of my AGI. not sure if I count on depreciation possibilities.

I will really appreciate if someone advise on above question and help me understand.

Thank you