In which case it cannot make anything determined and is entirely consistent with omniscience.
Not necessarily. Or rather, if we interpret spacetime ontologically (or as ontic), then the future is only locally defined anyway. Even if we interpret it as a useful, epistemological model to describe reality but distinguish time ontologically from space, we are still left with instantaneity being locally defined and therefore time as universally describable only via Lorenz (or equivalent) transforms which treat time as non-fixed (and therefore, once again, a future defined locally). Thus all that we require is a restriction to a strict separation between past and future exactly like that used in modern physics: defined in terms of light cones or some similar causal constraints. As omniscience is not causally efficacious, it no more determines the future or even describes the future than does the fact that there are stars which exist that we don't know of because there light hasn't reached the earth and those we believe to exist although they are long gone because light they emitted when the existed is still reaching us.
We aren't very good at understanding this distinction of future/past from a local sense (it is an intrinsic feature of language), but the "box universe" of an ontic 4D-spacetime entails that everything which happens both hasn't happened and will happen (is in the future and the past) simultaneously. Switch "spacetime" for an entity capable of viewing time as similarly static or as "outside" time (so to speak), and we allow for the logical possibility of an omniscient entity without a strict division into future and past and therefore without even fatalism, let alone determinism.
Yes. But in certain formulations, it is possible for the omniscient being to know everything that happens because time is linear and unidirectional only locally and the being is able to "see" the global "picture".
Or without a direction.
