You can use this.resetForm to (not surprisingly) reset the form.
Similarly, you'd use a custom calculation script in the field that you want to update depending on the value of the checkbox.
I do not know a way to clear the option (Radio) buttons on one button and then set them to No on another button; but I can clear them only or clear them and set them them to No on one button if that is any use.
First to clear all the option buttons:
1. Add a Push Button to the form.
2. On the actions tab of the Button Properties Select Action to Reset a form and click Add
3. On the Reset a Form Dialog just tick the fields that apply to option buttons and click OK
If you want the same button to set all the Radio Buttons to No then for each No button select "Button is checked by default" on the Options tab of the Radio Button Properties. Using the Clear Push Button set up above will then return the option buttons to their default value of No.
Not quite what you were wanting but maybe it will give you some ideas?
As to forcing the completion of a form field when an item is checked, there is no fool proof method, But one can set the text field's property to 'required' and then create a validation scirpt to check that all required fields are completed for a 'will save' or 'will print' action and take the appropriate action as needed.