A family of Microsoft word processing software products for creating web, email, and print documents.
Your description indicates that you are saving to OneDrive by default. You can change that in Word Options (File > Options > Save) by choosing the "Save to Computer" option and specify a local file location. Existing documents must be downloaded manually, though.
The prompts to sign in (to OneDrive) may be caused by added security. At least this is true if you are in an organization/business environment.