No, a rollover is not a new contribution. Don't enter under Deductions & Credits anything having to do this this distribution and rollover from the 401(k) to the IRA. Just enter the Form 1099-R and answer the follow-up questions.
No, rollovers from a 401K to a new IRA do not count as a contribution on your tax return. The 1099-R that you receive for the rollover should indicated that the monies used to fund the new IRA were a rollover. That is indicated on your 1099-R with a code G in box 7.