For non-physical things, such as emotions and thought... well, we have no actual proof they're anything but physical. We just don't have proof that they're entirely physical, either. But the simplest explanation is actually that they are completely physical processes and just as deterministic as everything else (which is to say, possibly not at all, depending on how QM is resolved).
[1] "Basically true" here means it's not strictly true (by that I mean it's not true in all possible cases) - but classical physics itself is not strictly true, thus relativity and QM... which are themselves not strictly true. We're still trying to find the theory that accurately describes all of physics.
Not the atoms of the neuron configuration etc., but the plane of existence where you place the red ball.
If we understood exactly where or how this plane exists and for whom, we could arbitrarily place objects and ideas in this plane. Eg force someone to think of a red ball bouncing, or pull imagined objects forcefully out of the plane.
Indeed: put them in a sensory-deprivation tank and show them a video of a (possibly simulated) ball bouncing. Their existing network of neurons will do the rest.
As I already said, though, that doesn't mean we should assume there's something metaphysical going on. When I think of a red ball neurons fire. We have no reason to believe there is anything else going on because we have no evidence one way or the other. The experience of thinking of a red ball is not evidence that there's anything supernatural going on.
Probably.
The physical world may or may not exist out there entirely independent of mind phenomena but the physical laws are a mental model in order to understand the world, the physical laws arise out of the interaction between the physical world and the mind.
The operating order is like this: there is mind -> mind perceives world -> mind makes mental model that presupposes the perceive world is independent of mind -> mind tries to determine its own origin within that presupposition.
If you simplify to the most extreme degree you're not left with "the physical laws", you're left with "there is mind". As such, the burden of proof is on the side of the presupposition that the external world is entirely independent of the mind that perceives it.
There seems to be no reason to believe that it's not.
On the contrary it seems most plausible that everything, including emotions, thoughts, decisions, are just chemical and electrophysical reactions. Thus deterministic.