Does money automatically added to an IRA (associated with a job) by that employer, as I was paid, count as "me contributing to an IRA"? I didn't add to the IRA otherwise.

No.  Employer contributions are not to be entered as regular IRA contributions.  Also, enter amounts shown in box 12 of your W-2 only in box 12 of TurboTax's W-2 form, nowhere else in TurboTax.

Thank you!