In concurrence with the statement that Gene and Finny do become friends at the end of the novel: Upon his return to Devon as he traverses the campus, Gene remarks,
Everything at Devon slowly changed and slowly harmonized with what had gone before. So it was logical to hope that since the buildings could achieve this, I could acieve, perhaps unknowingly already had acieved, this growth and harmony myself.
Having made this remark after reflecting that he has a "well-known fear" preserved from his Devon days and that the couple of places he wants to see are "fearful sites," the reader understands that Gene's early relationship with Finny was not a true friendship, but one of rivalry and jealousy on the part of Gene. For, Gene has feared and distrusted Finny's noble nature that knew no pettiness. Gene has projected, instead, his own pettiness upon Finny so that he could feel justified in his performing above Finny in his classes. But, Finny did not care, so Gene could not be victorious in his created rivalry. In Chapter 2, he contends,
There was no harm in envying even your best friend a little.
When Gene is unable to outdo Finny's athleticism, out of his envy, he becomes sarcastic because he "recognized sarcasm as the protest of people who are weak." Having spent the summer "in complete selfishness," Gene forgets that Finny has practically saved his life by giving Gene his arm on the limb when he loses his balance. For, in his act of jealousy and pettiness after Finny keeps silent about breaking a school record, Gene jouses the limb to give himself an advantage because, as he admits right before this action,
He had never been jealous of me for a second. Now I knew that there never was and never could have been any rivalry between us, I was not of the same quality as he.
However, Gene finds himself "in a pool of guilt," and finds that he must confess to Finny. When peace deserts Devon, Gene finds himself engaged in his own personal war just as the war goes on outside him. When Finny asks Gene to play sports in his stead, Gene agrees, saying,
"...I lost part of myself to him then, and a soaring sense of freedom revealed that this must have been my purpose from the first: to become part of Phineas.
After Finny's tragic second fall, Gene apologizes abjectly: "I'm sorry...I'm sorry, I'm sorry." He accepts the responsibility for his act as "some ignorance inside me." Gene extrapolates his thought later saying,
...wars were not made by generations and their special stupidities, but that wars were made instead by something ignorant in the human heart.
This "something "ignorant in the human heart" has never been in Finny, who never hated anyone or was never afraid. But, Gene has feared and envied him because of Finny's nobility. Only when Gene learns to recognize the integrity of Finny, only when he realizes that Finny has never been his rival, only when Gene gives of himself to Finny can Gene become his friend as Finny always has been his.
I'm not sure what you mean by this question, but I'll try. We see Finny and Gene's friendship only through Gene's eyes, so we can only speculate Finny's feelings toward Gene on the basis of what he says, how he acts, and Gene's interpretations of his actions.
That said, their relationship is somewhat one-sided. Finny's friendship is unconditional. When he tells Gene that Gene is his best friend, he means it. Finny is loyal, trusting, and kind. He genuinely enjoys Gene's company and accordingly persuades the more cautious Gene to accompany him when jumping out of the tree, breaking a swim record, or skipping class to go to the beach. Gene, on the other hand, cannot control his jealously of Finny. He likes Finny, but he secretly would like Finny to get in trouble with the authorities. Finny is everything Gene is not: impulsive, charming, gregarious. Finny brings some excitement in Gene's life, but Gene cannot accept Finny's gifts without suspicion. Gene's feelings toward Finny are ambivalent at best.
His impulsive action to jostle the limb to cause Finny's fall is the result of Gene's mounting jealousy toward Finny. The rest of the novel concerns the two boys' journey to understand the truth about this incident, themselves, and each other. Ultimately, I believe they are friends. Finny does forgive Gene in the end; Gene tries very hard to atone for action.
I hope this helps.