Determinism: Is the future determined or not?

The key here is the word "determine" with two distinct but related meanings:
1. cause (something) to occur in a particular way; be the decisive factor in.
"it will be her mental attitude that determines her future"
2. ascertain or establish exactly, typically as a result of research or calculation.
"the point of our study was to determine what is true, not what is practicable"

Read these definitions carefully and notice how different they are. By determine do you mean 1 (cause) or 2 (ascertain)? There is a HUGE difference between causing future events of knowing what they will be.

The Universe operates according to Natural Law. Clearly, future conditions and events are dependent upon (caused by) the situation of the present. On the other hand, the "veil of ignorance" (uncertainty) built into Quantum Mechanics severely limits the ability of humans to KNOW the future. So the answer is: BOTH yes and no.

In the sense of definition 1, the future of the universe is INDEED determined.
In the sense of definition 2, the future of the universe is NOT determined.