I'd say, "No," to both.
Paedophilia is an orientation: a persistent preference for a certain type. A paedophile simply feels a stronger attraction towards prepubescent children than towards adults or adolescents.
The term "mental illness" is bandied around far too much; nobody seems to care what it really means. An illness is something that decreases your health. A mentally ill person is incapable of functioning normally within society. They might have trouble with simple tasks, they might have trouble communicating with others, or they might see or hear things that aren't there. A paedophile, on the other hand, can have the full set of mental faculties, and be a fully functioning member of society. If they choose not to reveal their preference to anyone, there is no way that anyone can even know.
Well, you could argue that reproductive sex is part of functioning normally within society. An *exclusive* paedophile, at least, would find that difficult, and so one could argue that exclusive paedophilia is a mental illness. However, this argument would also imply that exclusive homosexuality and asexuality were mental illnesses, too. I would not use this argument, because I do not consider reproductive sex to be an essential activity, but I think this boils down to a matter of opinion. Either way, a non-exclusive paedophile would not suffer this problem, and could not, therefore, be considered mentally ill.
As for the matter of choice, paedophilia is not something that people "do". Like anyone else, a paedophile cannot choose who to be attracted to. But like anyone else, a paedophile who finds themselves attracted to someone will choose whether to try for a sexual relationship with them or not. There is nothing compelling them to do so, other than the choices that they make. Now, it just so happens that choosing to pursue a sexual relationship with a child is generally considered to be highly immoral, and is illegal, too. A socially responsible paedophile - like a socially responsible person of any other orientation - will choose not to pursue any type of relationship that is illegal and immoral. That is to say, they do not choose their orientation; they just choose how they act on it.