How the brain is affected by Alzheimer's disease
Essentially, there's a net dysregulation of a number of genes where the additive effect of each dysregulation causes neurotoxic amyloid plaque formations, and neurofibrillary tangles of hyperphosphorylated tau protein. Not only so, these mutations induce calcium and cytokine dysregulation, and increase oxidative stress. 

Specific to molecular mechanisms of amyloid beta (abeta) oligomer toxicity, a good article here makes some good descriptions. For example, abeta can reduce copper and iron ions. Oxygen reacting with these reduced metals become reactive oxygen species. They also noted that abeta reacts with many receptors, like TLR's which ended up promoting JNK-mediated apoptosis. I'd give that article a read, and I'll try to get some molecular pathology mechanisms for other facets of AD on board here.

They can't generally be repaired because the issue is with genetic mutations, and some of the mutations engage in positive feedback loops with existing conditions that make a more pronounced effect. For example, tau protein is regulated in part by O-GlcNAcylation. This is like phosphorylation, but with sugar moieties, but it becomes downregulated when glucose is low, thus increasing phosphorylation on tau (Liu et al., 2004) . Mutations that affect GSK-3, insulin resistance and/or diabetes thus can play a role in AD pathogenesis.

Some data exists to show restoration of potentially AD-causing abnormalities involving HDACs. For example, abnormal HDAC2 in AD brains hypoacetylated promoter regions for some housekeeping and plasticity genes, and they rescued the AD phenotype by knocking down HDAC2 (Gräff et al., 2012) . These are of course mouse models typically.

As for question three, I really can't say except for stochasticity. I did a review for an undergraduate course that goes over some of the recent literature involving AD genetics/pathogenesis. It might not be professional quality but it gets the message across, linked https://drive.google.com/open?id=0BwKiapIJL9T2ajc4ajhTVVRvRWc