Bitul Chametz (nullifying leaven bread)

It is a true point that Tosphot holds Bitul Chametz (nullifying leaven bread) is from hefker הפקר (abandoning) as he says in Pesachim page 4.
That is he holds that when we say on the day before Passover. "All the leaved bread or leaven itself that I own is הפקר (abandoned) like the dirt of the earth," we mean it is הפקר (abandoned). I do not have any Gemaras to be able to look up anything, but off hand I think we can see plenty of questions that just jump out at you even without thinking. First of all the dirt of the earth is not הפקר abandoned. Almost all wars in human history are fought over the dirt of the earth--land.
But that is not all. Neither Rashi nor the Rambam hold from this idea of "hefker." And from what I recall there is some kind of argument in Nedarim if Hefker needs to be in front of a witness.
And  a further question comes up is what about יאוש [letting go] which comes up about lost objects? Is this hefker here in Passover the same kind of thing as "giving up" on a lost object?
That is,-- with lost object we do not need the guy to be מפקיר. Just the fact that he gives up, that makes picking it up not longer in the category of stealing.
And what about that long Tosphot in Ketuboth about when we say דברים שבלב אינם דברים? {"Things in the heart are not things".} While here we say מבטלו בלבו ודיו he is nullifies it {the leaven} in his heart and that is enough.
The questions just keep piling up. What about that whole Sugia in Pesachim circa 93-94 where the Gemara says one does not get מכות (lashes)  because it is a לאו ניתק לעשה?

Incidentally, that whole thing about דברים שבלב אינם דברים comes up about a fellow that wanted to go to Israel and sold his property with that in mind and then changed his mind. The question there comes up in terms of when do we say things in the heart are not things--and  if there was some condition on the sale then he needed to say it and when do we say one needs a תנאי כפול כבני גד וראובן
[Sorry, I do not remember where that Tosphot is. Last time I saw it I was in Israel in Netivot and I wanted to look it up concerning אין אדם מקנה דבר שלא בא לעולם]
I seem to recall that Tosphot said we only say דברים שבלב אינן דברים only when his heart and his words or actions contradict each other-so that would at least take care of one of the above mentioned questions.

 I mean to ask if  ביטול חמץ is from הפקר and is a fulfillment of  אך ביום הראשון תשביתו שאור מבתיכם then how is this an מצוות עשה?
In any case the opinions of Rashi and the Rambam here also need some work.