Deterministic systems are mathematical models, so by definition yes.

Only if you know the initial state of the system and can describe the evolution of the system.

Deterministic systems are systems where any "future state" is a fixed function of the "initial state". If the observer knows both of these things, then it's predictable by definition. That doesn't mean that an observer actually knows the initial state or what the fixed function is. Things can get a little complicated if the system includes the observer itself.

There is a question of is it even possible to know or approximate what the initial state of a system is? It's possible to have a system where there's a limit to how much information you can get about the initial state.

(There's nothing special about the "math" part, "math" is really just any language that describes something precisely.)