For U.S. adoption - you can claim the credit before finalization (or for a failed adoption) but you must wait one year after you incurred the expenses (so in your case, you had expenses in 2016 for adoption that has not finalized in 2017- you must wait to claim them on 2017 tax return).

Please select Adoption Credit and Adoption Assistance Programs link for details.

Can I claim her as a dependent?

If you do not have the Social Security Number for the child, you can use a 'Taxpayer Identifying Number' to claim a dependency exemption.

<a rel="nofollow" target="_blank" href="https://www.irs.gov/help-resources/tools-faqs/faqs-for-individuals/frequently-asked-tax-questions-an...>

"As a prospective adoptive parent in the process of adopting a U.S. citizen or resident, you'll need a taxpayer identifying number (TIN) to claim a dependency exemption and, if eligible, a child tax credit for the child who is being adopted. If as the prospective adoptive parent you don't have and are unable to obtain the child's social security number (SSN), you should request an adoption taxpayer identification number (ATIN) or individual taxpayer identification number (ITIN). Please note that you can't claim the child tax credit on either your original or an amended return if your child doesn't have an SSN, ATIN, or ITIN by the due date of your return (including extensions), even if your child later gets one of those numbers."

Can I claim her as a dependent if she has lived with us for all 3 months of her life?

Do you have his/her SSN or TIN?

No

If the majority of your expenses have not been during 2016, have to wait until Tax Year 2017 to claim all of the expenses for the adoption.

"The IRS consolidates a majority of the reporting for adoption-related expenses on Form 8839, Qualified Adoption Expenses. Filers must include every qualified expense from the tax year in question on that form to be eligible for the non-refundable adoption tax credit. For 2016, the maximum credit adoptive parents are granted is $13,460 per eligible child."

<a rel="nofollow" target="_blank" href="https://turbotax.intuit.com/tax-tools/tax-tips/Tax-Deductions-and-Credits/New-Addition--Adoption-Tax...>

Depending on how far along you are in the process, its possible you can fill out Form 8839. <a rel="nofollow" target="_blank" href="https://turbotax.intuit.com/tax-tools/tax-tips/IRS-Tax-Forms/What-Is-IRS-Form-8839--Qualified-Adopti...>