USCIS didn't accept the filing because the form wasn't signed where required. A rejection isn't a denial: the case was never opened for review.
USCIS usually returns the package. Sign the current version of the form, check the fee and the rest of the package, and file it again. Mind any deadline that applies to you.
Informational only, not legal advice. Go by the notice USCIS sent you, and confirm deadlines and options with USCIS or an immigration attorney.
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No. A rejected filing was never accepted for processing, so there's no decision against you. You fix the problem and file again.
Sign in every signature box that applies to you, by hand, in the applicant's section (and the preparer's or interpreter's if someone helped). Check the form instructions for who must sign.
Generally no. A rejected filing isn't considered filed, so the new filing gets a new date. If a deadline applies to you, refile quickly and get advice.