That's sort of a weird scenario, but I'd say no - sending the bomb in the mail should have been illegal in the country they sent it from, whether it's illegal or not in the destination country shouldn't matter.

And if it isn't?

I'd imagine that mail services of other countries would refuse to accept mail from a country where it's legal to send mailbombs. If they didn't, I'd expect them to be at least somewhat liable for the ensuing explosions.

Countries don't arrest/extradite people for actions that aren't criminal in said country.

Depends on whether the person is wanted in another country and whether the governments of the two have extradition treaties that would apply. Many do.

A dangerous line of thinking.... If someone were to take prescription meds that's legal in the country they bought and took them, why should they be extradited to a country that happen to not agree on the legality of those meds?

That is only analogous if that person were facilitating the transport of these medications to a country in which they were not legal.