What is the effect on Harry of the attacks on Hermione?

To make him stronger and more resolute.

Therefore, why is someone attacking Hermione?

Because they want Harry to be stronger and more resolute.

Dumbledore and Quirrell want that. They have both been specifically training him for it, each in their own way. Did they arrange H's death?

No. Quirrell's dash to the scene and the conversation of Dumbledore and Quirrell about Harry after H's death indicate that they are afraid of what this experience will do to Harry. Therefore they are not the ones who arranged it. The only other person strong enough to be the agent behind Hermione's death is Voldemort.

Harry and Voldemort are enemies. Why does Voldemort want Harry to be stronger?

Because Harry is Voldemort's intended heir.

Why does Voldemort want Harry for his heir?

Dumbledore's talk of heirs to Harry alludes to Voldemort. Harry, as transformed by the experiences Voldemort is forcing on him, will be the person Voldemort would wish to be. In addition, Harry's scar is a horcrux of Voldemort. That is the spell that Voldemort cast in his confrontation with the baby Harry. The Killing Curse was directed not at Harry, but at Lily, to provide the death magic to create the horcrux. Voldemort intends to not merely be succeeded by the forcibly matured Harry, but to be him.

Dumbledore and Quirrell are also trying to develop Harry. Why not just destroy him instead? Quirrell at least would think of that at once.

Both sides want Harry as a weapon in the war.

What is the prize in the war? Surely nothing so trivial as ruling the world? Harry's own aims are far above that. Since arriving at Hogwarts, he has aimed directly for the heart of magic, using all the methods that wizards know nothing of to figure out how it works, and aims to remake the whole universe according to his desire.

That is the prize: the unification of magic and science, which will unleash power such as the world has never seen.

The secret that this is possible cannot be concealed for ever. Those in power have tried concealment: that is why Magical and Muggle Britain are so sealed off from each other. How could either side know so little of the other, when they live side by side, and everyone at the top level is familiar with both? Propaganda, lies, and concealment both magical and Muggle, to prevent people from learning the dangerous secret, convincing scientists that magic does not even exist, and wizards that science is useless.

It was not always so. Before Science, there was no need. When Science got started with Roger Bacon (his diary is an Important Object in the story, a Chekhov's Gun which has not yet been fired), someone in the wizarding world eventually realised the potentialities. It cannot be stopped: once a single person discovers the idea, someone will eventually do it. Only the agreement of the most senior wizards to not go there kept it from happening, until Voldemort defected. That is what the wizarding war is about. It was Dumbledore's plan that Harry Potter should be the one to make that unification of science and magic, and use it for the light side. So he was bred for great inborn magical power, given a scientific education, and then brought to Hogwarts while still immature, that he might be moulded to the cause.

The Singularity is approaching. Dumbledore and Quirrell are striving for a Friendly outcome, while Voldemort wants to be the outcome.