Sister and I inherited a house. We sold it. We each received a 1099-S. When answering TT questions, do we each divide the Cost basis and eligible deductions in half?

yes, split the tax basis in proportion to gross sales price on the 1099-S.  the "cost" is its FMV on the date of death of the previous owner.   special reporting may be required if either you or your sister used it as your personal residence or it was rental property.  

Yes, split the cost basis and eligible deductions (selling expenses) 50/50. 

The basis of property inherited from a decedent is generally one of the following:

1. The fair market value (FMV) of the property on the date of the decedent's death. or
2. The FMV of the property on the alternate valuation date if the executor of the estate chooses to use alternate valuation. See the Instructions for Form 706, United States Estate (and Generation-Skipping Transfer) Tax Return.

Related information: Where do I enter the sale of a second home, an inherited home, or land on my 2021 taxes?