Yes, you will need to pay Self-Employment tax, no, you can't include it as personal income.
Yes, you still materially participated in the business.
Unless you used accrual accounting where income is recognized when earned, you used Cash Accounting (which most people use) and income is recognized when paid.
It is unfortunate that they paid you in the following year, but that is when you need to claim it.
Paying Self-Employment tax is not much different than when the FICA tax is taken out of a W-2 Employee's paycheck. You do pay both halves as a Self-Employed taxpayer, but you also get a credit for half the Self-Employment tax paid on your federal return.
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