MW13, Yes, I am aware that the Rambam defines apikorus differently in Hilchos Teshuva than in Hilchos Avodah Zara. See the nosei keilim who debate whether there is any possibility of doing teshuva under either definition. Nevertheless, one can say that one who denies Techiyas Hameisim is claiming that there is no eternal reward, therefore why should I do mitzvos; I might as well be hefker. I still believe that there must be some nefarious motive to be a bona fide apikorus, not just a matter of innocent beliefs that do not ever translate into actions.
Your second question about the akeidah is a very good one, and one that has bothered me. I asked my family what amounts to the same thing on R”H at the meal. Why did Avraham not daven for his son Yitzchok to try to save him from the Akeida the same way he davened for the chotim of Sdom? Was his son any less worthy? Second of all, he had some very good arguments that he could use about Yitzchok, first, Yitchok was a tzaddik, not like the anshei sdom; and in addition, Avraham could say my whole life I have been preaching against child murder in the name of religion like the Ovdei Avodah Zara do to molech and other gods. I have taught that G-d wants menschlachkeit. Now, by telling me to offer Yitzchok, you are making me look like a fool and a liar, when my G-d also wants a child sacrifice. All my converts will now leave me in droves.
But we do not find that Avraham argued or davened in any way. But what is very interesting is that in the end, the RBSH was maskim to these unargued points, and taught us that he does not want child sacrifices, only menschlachkeit, like Avraham had been teaching all along. So possibly, Avraham thought that had it been somebody else’s child, he would have argued his head off. But for his own child, he had no right to, as it was a personal test. Nevertheless, in the end, the maskana seems to clearly be like I have been writing here all along, that menschlachkeit is the ikar.
I admit this is still very confusing, but that is how I understand it.