Pokemon obviously would age and die. I'm doubt that the Pokemon Tower, Mt. Pyre, and every other Pokemon cemetery are completely comprised of Pokemon that were killed by people, other Pokemon, or some other non-natural cause.
As for inside of a Pokemon, I don't think time stops for them. It's said that Pokemon train within their Pokeballs, and not only that, if time was stopped, Pokemon wouldn't be able to release themselves. To them, they'd be in their Pokeballs for a split second before being released again, they wouldn't simply be able to release themselves at random times.
Pokeballs take the makeup of a Pokemon, convert it into an energy, and keep it inside of the Pokeball. I'm guessing that's what the glass panels inside of a Pokeball are for--to continually reflect the energy within the Pokeball and to keep it from simply leaving. When a trainer releases a Pokemon from it's ball, a mechanism within the Pokeball opens. The Pokemon in energy form can come out (either by being shot out through the opening, or by just simply being released), and the energy comes back together to form the Pokemon. It wouldn't have aged, since energy can't really age.
But then again, I pulled most of that out of my *****, so you don't have to believe it. It could very well be that the Pokemon is converted into an energy, and once inside the Pokeball, it's converted again into a data form, until it's released and converts again into an energy, and then again into a physical body.
Either way, inside of the Pokeball, the Pokemon never ages.