I'm beginning a tax return for my mother,who died last year. Turbo tax keeps asking me questions about my "spouse". How do I respond to this?

You answer all the questions as if you were your mother. Did she have a spouse, was he alive at the time, etc.

very important! You can only file one return per account with TurboTax online. If you are trying to use the same account for your mother as for a return you already prepared, then you are just over-writing the old info, and you will not be able to file, plus you are erasing all of your own old info. You need to make a brand new account with a new username and password and start from scratch to file a return for somebody else in the online program.

I'm sorry for your loss.

How do I respond to this?

Depends on what the specific ane explicit question is. You didn't tell us.

Sounds to me like your mother is filing as married filing separate. If your father is still living, may I ask why? If not filing MFS, then what is her filing status?

The absolute only way the program will ask for your mother's spouse information would be if she was filng married filing joint, or married filing separate. If your father was not living in 2019 then her filing status must be single. If your mother had a qualifying dependent in 2019 then her filing status could also be Head of Household. But for both Single and HOH the program does not ask for spousal information.