I'm not a neurologist but I was (before I retired) a medical doctor and have covered aspects of neurology in training and in work. The contents of the hospital letters gets raised quite frequently so I thought I'd try to explain more. Skip this is you don't want a neuro tutorial!
Symptoms and signs are different things. Symptoms are what the patient compains of - and in neurology, they can be many and varied, and of course no-one but the patient can know what things actually feel like to them. The 2nd paragraph in the 2015 letter lists the symptoms.
Signs are what an outside party can see or elicit. Some of these can be faked (eg you could imagine you could hold a limb very stiffly out of choice), some would be much more difficult to fake.The third para in the 2015 letter is about this. An experienced neurologist should have a good feel for genuine signs, and there are little "tricks of the trade" that can sometimes help distinguish between genuine and fake.
Looking at the signs: firstly, Parkinsons disease and similar states often affect a person assymetrically, and usually lead to reduced voluntary movements. So reduced L arm movements is entirely possible. The "myoclonus" refers to that irritating involutary muscle twitches that we all sometimes get, not a bigger jerking movement; I can't think how you'd fake myoclonus. "Abnormal posturing of the left hemibody while he walks" fits with his illness but is it for real? I haven't seen TW bending or leaning awkwardly in any pictures or videos. Ideomotor apraxia would be pretty easy to fake; stereognosis ditto. Basically these mean that he would find it difficult to repeat demonstrated movements, and to recognise position of parts of the body (shut your eyes, ask someone to move your toe or your thumb - you know what position you're holding it in even though you can't see it. Neuro damage can mean that the brain can't tell the position). Saccadic eye movements are very quick and brief flickering movements of the eyes as they move; I don't think you'd be able to fake those. So we really just have the eye movements and myoclonus. Hardly severe, hardly a terminal state.
By 2019, he's had a scan which shows "dopaminergic depletion" - ie less of the chemical dopamine that you'd expect in the brain, and this gives weight to the idea of a Parkinson-type illness. He also has "atypical disturbance of the anal sphincter function" - let's not go into this too much! It could be neuro - but usually it's not!
It sounds from these letters as though there's been virtually no neurological disease progression over the years though clearly TW has had some more recent heart problems.