The so-called glymphatic system, pump washing the brain with cerebrospinal fluid during sleep, has already been mentioned in answer to the SE question "Do you need to sleep every night?" It seems more than just a memory cleanup process as if on a computer, but "has significant implications for treating 'dirty brain diseases like Alzheimer's" and understanding it "is a critical first step in efforts to modulate this system and make it work more efficiently" (Maiken Nedergaard). That should go towards answering Q2, at least if such interventions take place in the waking state at the experimental stage.
Another recent report concerns brain cells known as microglia, which also play a role in mopping up neurotoxic brain waste such as beta-amyloids. In addition they monitor the growth of synapses and prune connections between neurons so that the brain can refine its circuits and conserve resources, particularly during adolescence. Relevant maybe, as this is a period in life known for prolonged sleep. Some research on mice suggests a preference on the part of microglia for carrying out their work when the organism is in darkness. Hyperactive microglia however are conjectured to be implicated in Alzheimer's by stripping too many synapses when these are inadvertently tagged by the brain for destruction.
"To Sleep, Perchance to Clean. Study* reveals brain takes out the trash while we sleep" University of Rochester News Room 17 Oct 2013
*Nedergaard M (corresponding author) et al "Sleep drives metabolite clearance from the adult brain" Science 18 Oct 2013
"The Mind Minders - a fertile, flexible brain couldn't live without its roving band of caretakers". New Scientist, 12 Oct 2013.