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Yes. A separate DS-160 must be filed for each person applying for a visa, including infants. See, for example, this page: "[A]ll children need a visa for travel to the U.S." And you will need to pay the applicable visa fee for the child's nationality and visa type just like any other applicant.
Check the details on the website of your local consulate, but children 13 and under generally do not need to appear for the visa interview.
The US Department of State has some tips on taking photos of young children for this purpose.
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The CGI Federal web site calculates all fees automatically and asks you to enter receipt numbers for all family members.
However, one person had a problem when the web site asked to pay more.
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Yes, I'm afraid so if your baby requires a B-1/B-2 visa, with some very exceptional exceptions. The current Nonimmigrant visa application processing fees (non-refundable) for all categories are set out here. Depending upon nationality a Reciprocity fee may be payable in addition.