If $$G$$ is a context-free grammar and $$w$$ is a string of length $$n$$ in $$L(G),$$ how long is a derivation of $$w$$ in $$G,$$ if $$G$$ is Chomsky normal form?

Context-free languages are

In which of the cases stated below is the following statement true?
“For every non-deterministic machine $${M_1}$$ there exists an equivalent deterministic machine $${M_2}$$ recognizing the same language“.

Which of the following statements is / are true / false?

The language $$\left\{ {{0^n}\,\left| {\,n} \right.} \right.$$ is prime$$\left. \, \right\}$$ is not regular