I received some money from selling my half of out house to my ex-husband through the divorce settlement and got interest on it. How should I file this 1099?

You can enter it by clicking the following:

• Federal
• Income
• Show more next to Interest and Dividends
• Start next to interest on 1099-INT

This interest is taxed as ordinary income, which is the same rate your wages or salary is taxed at. 

and what if I gave some money as a gift to my daughter's down payment on her new house?

The interest income would be reported the same, whether you turned around and gifted your daughter or not. 

As a side note, if the gift was over 18,000 for tax year 2024, you may need to file a gift tax return, Form 709 which is separate from your tax return and is not supported in TurboTax.