Yes, you have a choice and can choose the year you want to use the carryover for the future year.
That choice would be made when filing.
Once the years allowed for that carryover are exhausted, any remaining carryover is lost.
How a charitable contribution carryover is handled is actually pretty complicated.
The order a carryover and new donations are claimed have a certain hierarchy depending on type of donation and type of charity.
Here is an IRS link with more
Yes, TurboTax will carryover the unused amounts and apply them to subsequent return.
You can always check under
Deductions & Credits
Charitable Donations
Charitable Donation Carryover from (previous) year
Here is a TurboTax link with more
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