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For your first question, hoaprez3 is correct. You prolly do need to organize as a nonprofit corporation under state law.
As for your second question. yes HOA’s do need to pay and file tax returns. Just cuz you are incorporated as a nonprofit doesn’t mean yo0u’re automatically excempt from taxes. To qualify as a tax-excempt nonprofit, you must meet the IRS requirements under 501(c)(4). On a federal level most file Form 1120-H or 1120. State tax forms can vary so best to check that out your self.