Why does my attempt at RSA break? I have that $N = 798$, $p=2$, and $q=399$. I choose $e$ such that $\gcd(e,(p-1)(q-1))=1$ where $e=7$. I, then, choose $m = 123$. Thus, $c=123^{7}\bmod798=669$, which is my ciphertext. After, I try $d=7^{-1}\bmod398=57$. I, then, get the wrong result that $m'=669^{57}\bmod798=729$ which is not my original message $m$.

Why is this? I can't seem to understand why RSA would break. Does RSA break if either $p$ or $q$ is 2 and the other is a composite?
Since your q is composite with factors 3,7,19 we get $\phi(q)=(3-1)*(7-1)*(19-1)=216$ and not 398 The rest of the calculation follow as in the question. 

And since $p=2$ we get also $\phi(n) = 216$

As a result we also get $d=e^{-1}=7^{-1}=31 \bmod 216$

And we can verify that $669^{31} \bmod 798 =123$ as expected.