"self-Determination" and "decision-making" are conscious, complex processes. A single cell is incapable of that.

On the other hand, how do we as humans form decisions? We use sensory input from various organs, process those by combining with existing knowledge/memories and form decisions based on that. But in the end, it's still all based on "chemical and mechanical reactions".

You quickly get into philosophical territory there: is our conscious self more than the sum of all the processes in our brain? Is there some extra "spark" that allows true self-determination, or are all our decisions a given result of the exact state of our brain and body?

The function is in the interconnection and collaboration of the parts of the system. A screw or a round rubber also doesn't drive you to work. It's the whole car consisting of several parts that work together that does it. Also a single cell is a tiny part. There isn't much in a single cell if we look at a complex process like making a decision.

Immune cells form from stem cells. From start to finish in the stem cell differentiation process, four major changes occur. Some of these changes can have up to four potential outcomes each. Here's a map:

While all cells react to their environment based on environmental stimuli and feedback loops, even bacteria and archaea, this is a great example of cell differentiation. All our cells started as stem cells, but the immune system's continuous and consistent use of the process is very unique. It's also the most elaborate and the image is surface level. Most the end cells pictured here will become more specific. Like there's many different T-cells, even T-cells which change so much they don't meet the classification of being a T-cell. The CD16 T-cell is a great example of this happening.

I feel like this is what you were looking for, but I'm not totally sure.

Just to spur this question on a bit, I know from my limited knowledge that cells can kill themselves when a mutation has occurred. But that's also a sort of biochemical reaction. To be honest, what is truly self-determining? Is it simply a property of the nervous system? My thoughts are leading in that direction to be honest.

There are good answers about differentiation from stem cells, process governed by the evolutionary determined genetic information stored within the cell itself. This genetic information was/is influenced by environment but that influence tends to be slow and subtle.

I have another answer to contribute. Metastatic cancer cells. These are cells which detach from primary tumors in any part of the body, then have to break into the lymph or blood and then they in a sense "decide" where they want to settle. We now know they'll have preferences: some cancers will metastase to liver, some to lung, some to brain; but before they do so, these cells will literally circle around the body, searching for a "perfect spot". Once they find it, they settle, often entirely changing their O.G. tumorous behaviour in the process which in return makes them super unpredictable and hard to kill. And all it takes is one wandering cell.

A "decision" is highly complex emergent behaviour. Looking for it in a single neuron is like asking if there's a single air molecule where a gale started. We almost certainly will never identify single neurons corresponding to single mental ideas. A "go to the cinema" neuron versus "go to the park" likely don't exist. What is more likely is that large 'flows' of neutral activity correspond to these things or to what we call 'decisions'. However when we think of more and more specific mechanical things (like lifting a finger) then it's more likely this corresponds to very small areas of neurons that controlled their activation and it makes a bit more sense to talk about that being a switch to 'decide' to move a finger. But the decision itself is actually the vast cloud of neutral activity leading into it not a single thing.