Pesachim 21: Chametz Liability

Anytime that you are allowed to eat chametz, you're also allowed to get benefit from it in a variety of ways (or all ways). What happens in that in-between time of the 5th hour, as per the debate when you must stop eating chametz (4th or 5th hour)? Also, what is this formulation of "permitted to eat" and "to feed"? Also, selling chametz to a non-Jew during that same time that you can still eat chametz (which is getting benefit from it, if course). Which leads us to a dispute between Beit Shammai and Beit Hillel that has far-reaching implications, or would if we paskened like Beit Shammai (we don't).