Your 1099-MISC income is reported on a SCH C as a part of your personal tax return. You are considered self-employed as far as the IRS is concerned, for your 1099-MISC income. You will have to upgrade to the Self-Employed version, as you can't report self-employment income with the free edition.
Yes, if your child was born at any time in 2016, even at 11:59 on new year's eve, you select that the child lived with you the whole year.
