Question 1: Who is our hero in this film? Frodo or Sam?
You are right in that Frodo could at the end not withstand the power of the ring and was corrupted like all the others. Only once the ring was destroyed was he free of his desire for it. This way Sam could indeed be seen as the true hero, always loyally holding to Frodo and not falling to the power of the ring.
Yet I'm not sure this matters so much. Yes, if seeing it that formulaic you could maybe call Sam more a hero than Frodo was. But then again Frodo was the Ring-bearer (and not the "ring-carrier") and suffered heavily from this burden, carrying it all the way to Mordor (to its final destruction). Does that weak moment at the end where he finally couldn't stand the influence of the ring anymore make him not a hero and annihilate all his achievements? I for myself don't think so. He contributed as much to the destruction of the ring as all the others.
In the same way Frodo or Sam are not alone responsible for the victory over Sauron. Many others were too, be it Gandalf, Aragorn, Merry, ... There are just many heroes in the whole story, and not any of them is without flaws or weaknesses. I therefore would not see the whole story (even though it is pretty much about good vs evil in its purest essence) in such a narrow way as to who is more of a hero than others. But if you want to see it that way, I could agree that Sam might be considered the true hero of this story.
Question 2: Why does Frodo deserve immortality by going to undying land? Why is Sam not qualified for this journey?
First of all, as explained in this question and its answers, Frodo and Bilbo were not going to live forever in the Undying Lands, they just got a very nice retirement place. Neither do I think it was for their achievements in general, but rather because they were Ring-bearers (as well as the other people on the ship, if considering the three Elven rings, too). After all, Bilbo didn't directly contribute that much to the Ring's destruction either.
But even if Sam would have been offered the chance for that journey, I'm not sure he would have gone. He had a very happy life in the shire to look forward to, together with Rosie and their family.
How do you pick up the threads of an old life? How do you go on... when in your heart you begin to understand... there is no going back? There are some things that time cannot mend... some hurts that go too deep... that have taken hold. [...] My dear Sam. You cannot always be torn in two. You will have to be one and whole for many years. You have so much to enjoy and to be and to do. Your part in the story will go on.
It was Frodo whose soul was struck by his journey deeper than it could recover (and who in this way probably paid a much larger price for the victory than Sam did, no matter what exactly happened at Mount Doom) and who didn't see much of a future for himself in the shire (and maybe the ones that granted him his place on the journey sensed that, but this would be speculation):
Frodo: We set out to save the Shire, Sam. And it has been saved... But not for me.