I. All that is needed is a supply of oil.
II.All what is needed is a supply of oil.
I understand the first sentence is perfectly right. How about the second? Is it wrong or just less grammatical? Please.
I. Having been ill for a long time, he tried his best to finish his book.
II. Being ill for a long time, he tried his best to finish his book.
Are these two sentences right? Do they mean exactly the same? Please.
To answer your first question - I feel the second option is just wrong.
As to your second question. For me there is a difference in meaning.
The first could be used to indicate that 'he' was now well again and so could continue writing his book
The second might be used to indicate that 'he' was taking advantage of (for example) the extra time now available to him because he doesn't have to work while ill and so can finish his book.