I try very hard to find a satisfying "derivation" of the relation $E=mc^2$, but it turns out that everything is circular. For example, under this answer, my2cts points out that if you assume $p=m\gamma v$ then classically we have $E=p/v$, which inevitably leads to $E=\gamma m$. (Here $c=1$.) Of course $E=mc^2$ can be backed up by a physical argument - see Einstein's original paper - but if we want to derive it mathematically, it turns out we need to assume something like $p=m\gamma v$, and I don't know why we should have such definition. (It is the spacial part of 4 momenta, of course, but why should it be 3-momenta as well.) Here are my questions:

1. Why my2cts say that classically we have $E=p/v$? I do not completely understand it.
2. Is $E=mc^2$ just a sensible definition made according to de Broglie's interpretation of momentum of electron $p=\hbar k$, and cannot essentially be derived?