Parkinsons have tremor at rest, with slowness of movement.
Your father, has tremor while doing an activity. It could be due to cerebellum involvement.
Slowness while walk could be due to fear of falling down.
Does he walk slowly with a wide gap between his feet?
Has he experienced any fall recently?
Any difficulties while talking?
Has the size of his hand-writing increased?
Next Steps
you will need to seek a neurologist consult.
mri brain after neurologist opinion may be required depending on the physical examination of the patient.