Yes, you can claim the points in full on a purchased home (your duplex). Deducting over the life of the loan refers to refinancing points not used for purchase or home improvement. Just select the box I bought or improved my main home with this loan in 2016, when going through the mortgage interest data entry in Deductions and Credits.
As to the half rental property... you should divide your expenses between rental and duplex. Half of mortgage interest, real estate taxes, points, mortgage insurance is entered as your rental expense, the other half under personal deductions and credits.
Other expenses, such us utilities, HOA, hazard insurance etc. should be also divided in half. The rental half is your rental expense, the other half is not deductible at all and not entered anywhere, as these listed expenses do not qualify for personal deductions.
