In what time frame can the rabbi sell the chametz. I don't mean when the contract is drawn up, but when the non jew actually takes ownership. Can the rabbi sell the chametz like a week before pesach or before bedikat chametz i.e. is there some limit, before which he cannot sell it?

Am I corect in thinking that the chametz that is sold does not include the chametz left inadvertently aroudn the house. Otherwise - i.e. if that chametz left inadvertenetly aruodn the house was sold, then we couldn't then burn it and declare the rest ownerless. Or, if we burnt it, then declared the rest ownerless, we couldn't sell the rest, because it wouldn't be ours to sell.
Based on that reasoning, that the chametz is different chametz. Am I correct in thinking that it doesn't mater if it's sold before bedikat chametz, or between bedikat chametz and burning, or after burning. As long as it's sold by a certain time during erev pesach. I would actaully think that it can be sold a week before pesach, but i'd like to check is the case,

I have haerd that the time limits are
4h we finish eating. 5h we burn. 5h rabbi sells
Where 4h is the 4th jewish hour (after sunrise?), e.t.c.
Are all of those cases, *By* the nth hour, or *During* the nth hour? For example, must the chametz be burnt during the 5th hour and not before, or can it be burnt immediately after bedikat chametz?

in all cases when i say 'sell' i mean the contract going into force, i.e. the non jew taking possession of the chametz.

thank you!!, shalom

If i remember correctly, the Rabbi who "sells chometz" to the Non Jew is just collecting contracts from people and that the sale only takes effect when one can no longer own chometz.

Yes, you can sell before Bedikas Chameitz, and some hold that you're obligated to sell before the time of Bedika, so that the obligation of Bedika Shouldn't be on those places (If it's not sold yet, then all those chometz is yours and needs to be checked)

The hours are Shaa Zmaniyos, according to the length of the day

It shouldn't be burned at night, since burning is learned from Nosar (leftover karbonos) and they can only be burnt by day.