Do you blame Gene for Finny’s death? Why or why not?

I guess that I would have to say yes, Gene was responsible for Finny's first accident. He jounced the tree limb, he caused the fall.

....Holding firmly to the trunk, I took a step toward him, and then my knees bent and I jounced the limb.

Finny falls the second time, rebreaking his leg, after hearing the witnesses at the mock trial. Once again, Gene is indirectly involved in the accident. Gene didn't, of course, ask for the mock trial..... nor did he want Finny to hear what was said, but it was something that Gene should have made Finny understand previous to the other boys putting him on the spot. After this second fall, Finny dies when a piece of marrow strikes his heart during surgery..... marrow that broke loose from the bone that was rebroken when Finny fled, and ultimately fell down the stairs.

Gene himself takes the blame for Finny's death in the novel's last chapter.

I never killed anybody and I never developed an intense level of hatred for the enemy. Because my war ended before I ever put on a uniform; I was on active duty all my time at school; I killed my enemy there.