No. Death-Mask Duplicant only allows you to copy the effects that are explicitly listed on it - flying, fear, first strike, double strike, haste, trample, and all forms of landwalk and protection. Exiling Platinum Angel would only give the duplicant flying.
No, Death-Mask Duplicant does not copy any abilities.
It has an ability that can grant it other abilities, and those other abilities are listed in the text: Flying, fear, first strike, double strike, haste, landwalk, protection, and trample. The abilities of the imprinted card are not copied or given to Death-Mask Duplicant. Rather Death-Mask Duplicant conditionally has the listed abilities.