Is 'できなく' converted from 'できない'? I've learned adj. '..い' can convert to '..く' in this case. Does verb's 'ない' form also have such transformation?
Does verb's 'ない' form also have such transformation?
Yes. ない behaves just like an i-adjective. And the continuative form is なく just as you'd expect.
As you may already know, to say 'becomes adjective' you replace the い of an i-adjective with く and the な of a na-adjective with に, then add なる.
So できる (can do) -> できない (unable to do) -> できなくなる (become unable to do).