Decidability of Machines
As a result, I can say that every NFA that can be constructed is decidable. Is this true?


Yes. An NFA can be converted to a deterministic finite automaton, and that can simply be run to decide the output.


  However, is it possible to find a Turing Machine that can accept w whose length is composite number?


Yes, this is possible. It follows from the fact that it can be done in any old Turing-complete programming language, hence also on a TM.


  Is it possible to construct a CFG that accepts this w?


I doubt it. Maybe there is a proof, but I do not see it right away.

Most problems you'll encounter in practice are decidable, because you can come up with an algorithm to decide the answer. If you want an example of an undecidable problem, have a look at this list on Wikipedia.