I think you'd be best going for a vampire made of 'utility fog' not unlike overwatch's reaper.
They can spread out to become invisible or move quickly through self generated air currents, or rearrange themselves to shape shift.
The machines can simply be replicated and added to the vampires fog allowing for immortality, (perhaps self-replicated or replicated by a few thousand mother nanites.)
They are compelled to count things because of a quirk of utility fog psychology or perhaps due to a (computer) virus that infected vampires a while ago.
They are damaged by sunlight because the small components of the nanomachienes are delicate and damaged by differential heating, or perhaps their fine circuitry gets fried by U.V. radiation.
The nanites are made of carbon, which is obtained from human blood as these nanites where first developed for medical purposes and were designed to use the patients blood to self-replicate.
Paleness is caused by a coating of titanium dioxide (very very heavy duty sunscreen) used to try and resist the aforementioned UV frying the circuitry. Though is obviously not 100% effective or perhaps is only effective when intact, meaning these vampires are only damaged by sunlight when scratched or when trying to spread out, shapeshift or use any other abilities.