When Hiro or Peter freezes time and everything around them stands still, how are they still able to breathe? Wouldn't all the molecules in the air be frozen in place as well?
In later seasons it is shown that they don't stop time, but slow it down to near-stopping.
The characters show that they are still able to manipulate their environment while using the time slowing power - no reason to believe they still can't breathe in the slowed air. If they can move someone, they can suck air into their lungs.
We find out, when Hiro meets Daphne, that he doesn't stop time. What his power allows is the manipulation of time.
What we see is Hiro slowing down time.
We could then argue that even though the natural motion is slowed down, once you try to breath it in it's freed and part of your environment (as an aside: How far out from Hiro/Peter does the 'time' buble stop? It feels as though there must be some leniency or else this situation would become a problem), in the same way as when they interact with objects and people without negative consequence.
I think the problem is that we are thinking about it literally, 'stopping time'. It should be impossible, for time is after all one of the four powers of the universe, and a constant.
So that leaves us with three possibilities for Hiro and Peter.
1) Enhanced Time Self-Manipulation - They're not 'stopping' time; they are accelerating it to a point to that it looks like time has stopped in their perception. It certainly kills the bubble theory (how horrible would that be if time stopped for only a certain distance!) and would explain how Hiro and Daphne (a speedster) could, in fact, interact. Of course, that means their reflexes, speed, perception, and interaction must accelerate as well, as opposed to just hyperperception. Extra perceptions are abound in comic books (of the top of my head, the She-Hulk was aware of trans-dimensional areas and happenings around her, though I don't know why). Deadpool, of course, is completely aware that he is a comic-book character with text boxes for thoughts and speech (known as the fourth wall). This could just be an extra perception power, but doesn't really explain teleportation... unless Hiro walked from Tokyo to NYC.
2) Possible Sub-Dimensional Travel and Interaction - A cute cheat on both teleportation and bi-dimensional interaction and manipulation of two separate dimensions interacting at once. While teleportation is mathematically possible (we've teleported light waves, btw), mass is tricker. Hiro could simply be shunting himself to a sub-universe that touches his own, where time/space is actually a variable, and not a constant. Thus, stopped time with interaction and the ability to breath, and the ability to move from one location to another without walking. Think of him popping into a photograph of the world that is taken them moment he activates his power, and the ability to move/do as he sees fit before popping back into reality wherever he wishes.
3) Master of the Time/Space Continuum
Seriously. Who needs to be Superman when you can do this? Admittedly, both Hiro and Peter have died while using their abilities to stop time and move without walking (Samurai Hiro is shot and killed by Matt Parkman, Scarred Peter is shot and killed by Claire Bennett, completely ignoring the fact that he can heal, illusion himself, and stop bullets), but this power is still incredible.
Of all this, the third seems the best. The worst explanation, but it fits, Occum's Razor style.