Okay, I'm no scientist, and my big degree was in English Literature, but I'm pretty sure I can answer these.
1. While we do not know for sure, we have some pretty good ideas that are better explained in number 2. Basically, inorganic chemicals combine under pressure into protein molecules that form RNA that form DNA that form micro-organisms. So the 'stuff' was just the right combination of chemicals on a primordial Earth.
2. http://www.pnas.org/content/112/3/657.abstract
Or, in layman's terms: http://www.iflscience.com/chemistry/scientists-form-building-blocks-life-recreating-asteroid-collision/
Basically, we can.
3. This doesn't actually have anything to do with evolution, though neither did 1 or 2 - evolution being the differentiation of species. Energy can't be destroyed as far as we can tell, but mass can be converted into energy, as in nuclear reactions, and thus it is presumably reversible. In that sense, matter is eternal, I guess? But again, this is physics, and is as relevant to evolution as gravity.
4. The cells and DNA don't change to adapt to the environment. It's way simpler than that. The horses move to a place where the trees are taller - be it because of predators, or drought, or many possible reasons. The short horses can't reach the trees and die off before they have kids. The tall horses survive. The only horse genes still around are tall horses.
Going further, the taller horses of these new generations get more food, because they can reach higher. More of them survive. More of the taller tall horse genes survive. The horses get taller as a species. Eventually they reach the tops of the trees and getting taller has no effect on survival rates, so their height plateaus. This generation looks very different from the horses that first arrived at the beginning of the previous paragraph. Might as well call them giraffes.
In answer to your other questions in this section:
Not all animals eat leaves. Not all herbivores eat the same leaves. If they did, it would be disadvantageous due to the competition for the same food, and species would die off, thus their genes would not be passed on.
Amoebas still survive in their own environments, so their genes still get passed on.
The amoebas that evolved to multi-cellular survived as well, so their genes also got passed on. The species diverged without one branch going extinct.
5. Maybe wings would be advantageous, but obviously you don't just spawn the DNA for wings. Wings evolve, just as long necks do. Horses don't have the requisite limbs to evolve into wings. For animals that might evolve wings but don't currently, look to the "flying" squirrel. It has webbed limbs that allow it to glide. Presumably the bat went through a similar evolutionary stage.
Horses, and humans for that matter, have no great need for wings, or for gliding, or for better jumping. None of these traits would improve our chances for survival, so the genes for them wouldn't outnumber the genes of individuals without them. Your hypothetical slightly webbed horse would have no significant impact on the species as a whole, while all those un-webbed horses are still surviving just fine and throwing their un-webbed genes in the gene pool.
Humans lost their hair to keep themselves cooler when they moved from the forests to the warmer Savannah. You'll notice that people from Africa tend to have less body hair than the humans who migrated north to, say, Scandinavia, where it's much colder.
6. Every species is in constant, agonisingly slow transition. Each generation is another tick on the clock. Every generation is a link. Every fossil is a transitional fossil.
7. See: food chains; migratory patterns; mating rituals; ecosystems.