Can I use separate or different voltages to power each side of the isolation barrier?
Can I use the Si86xx as a level shifter?
Each side of the isolation barrier is powered independently of one another.
Example: You can run a unit with VDD1 = 5.0 V, and VDD2 = 3.3 V, or vice versa.
So long as VDD1 and VDD2 remain within the specified range (see the data sheet's electrical specification table) you will be fine running them at different potentials.