Proving that the language of satifiable CNF formulae with primes is NP-complete
For 1): You have to prove that the language is solvable by a nondeterministic TM in polynomial time. The easiest way is indeed to use previously defined TMs, e.g. the TM to solve SAT. So your approach is correct.

For 2): You don't have to prove it for every $L'$ $\in$ $NP$ explicitly, it suffices to give a reduction from a language that is NP-complete. The idea is that you reduce every word $w' \in L'$ to a word $w \in L$, so if you find an efficient way to solve $L$, you also have an efficient way to solve $L'$. So you can choose any NP-complete language that should provide a simple reduction to $L$.

The next step therefore would be to choose such NP-complete language $L'$.

Next you have to find a reduction $f$ to reduce your previously chosen language $L'$ to your language $L$. Depending on your choice of $L'$, this can be a very simple process in your case. Note that $\{$ $f(w') \mid w' \in L \} \subseteq L$, not $\{$ $f(w') \mid w' \in L \} = L$