If the job you are taking will be reporting your income on a 1099 form, then they are classifying you as an independent contractor, which basically means that you are self employed.
As a self employed person, in order to take a deduction for your health insurance premiums against your income from self employment, the insurance plan must be established under your trade or business, and you cannot take this deduction to the extent that the amount of the deduction is more than your earned income from that trade or business. If you had such a medical plan established under your business, Form 1040 line 29 is where you would take that deduction.
Your payments for Cobra would not qualify as a direct business expense against your self employment income. You can, however, claim a deduction for your Cobra premiums on Schedule A for itemized deductions, but your total medical deductions must exceed 7.5% of your adjusted gross income before they become deductible.
As far as whether or not you can still collect unemployment benefits, the state of New York is one of the states that participate in the Self Employment Assistance Program.
Self-Employment Assistance offers dislocated workers the opportunity for early re-employment. The program is designed to encourage and enable unemployed workers to create their own jobs by starting their own small businesses. Under these programs, States can pay a self-employed allowance, instead of regular unemployment insurance benefits, to help unemployed workers while they are establishing businesses and becoming self-employed. Participants receive weekly allowances while they are getting their businesses off the ground. So chances are you may still qualify for benefits under this plan, but you would have to discuss your particular situation with a case worker with the NY Unemployment Division to get a determination.
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