How do I find if my tax preparer claimed depreciation for the years we rented out our primary home, which we sold in 2018? What impact would refinances have?

Depreciation is listed on Form 4562. Also look at line 18 on your Schedule E. (or line 13 of Schedule C)

Refinancing does not impact depreciation. Depreciation is based on the basis of the property. This is usually your cost at the time the building is put into service. It does not include the land, the land value is kept separate. 

Refinancing may affect the amount of interest you claim as an expense, and it may affect the amount of capital you have invested in the rental. The profit and/or loss of a sale would be the same whether it is completing financed, or own with cash and partial financing.