Can we say 'on' rather than 'about' in the below sentences?
Dont worry on this issue. [We 'worry' on something in the same way a dog worries (or 'worries on') a bone!).
I need your advice on this issue.
1. Don't worry on this issue. The problem here is not the preposition on itself but that the verb "worry" is usually collocated with about or over rather than on. This contrasts with "Don't worry on my behalf." in which the on is collocated with "my behalf" rather than worry. So your example is not a good one to show the use of on.
2. I need your advice on this issue.
3. I need your advice about this issue.
In broad terms, on tends to have the slight nuance of specifically; directly; exactly, whereas about tends to have the slight nuance of around; generally; in broader terms; as a whole, although I am not sure that everyone consciously makes this fine distinction.