I LOVE making layer cakes, so here is my take on them
You want the layers to be flat, but if you cut them, it's harder to ice without it getting all crumbly. They make a product called baking strips that you wet and put around the outside of the cake pan while baking, and these cause the cake to bake almost perfectly flat. Instead of buying them, you can make your own - just cut a thick towel into 1" strips, wet them, and pin them tightly around the cake pan. This makes my cakes bake so evenly that they don't need to be leveled.
Then, I prefer to brush the cakes with a liquid (kahlua, or either flavored or plain simple syrup), wrap them securely (I do 3 layers of plastic wrap and 2 layers of foil) and freeze for a day or two, or up to a couple weeks. This seals in the moisture and usually results in an even better textured cake. Plus you can get the cake-baking out of the way early. Then I let it sit out on the counter, still wrapped, until it's cold but no longer frozen. (Some people frost the cake partially or fully frozen, but I don't because I'm concerned about the condensation affecting the frosting.)
Once the cake is ready to be frosted, I assemble the layers and do the filling; I like to do semi-pourable fillings so that they go on easily. Plus it usually tastes better that way. My favorite fillings are caramel sauce, chocolate ganache, and fruit whipped cream. Then I crumb coat; I thin the icing quite a bit and apply it to the whole cake, making sure it gets on every exposed surface. This seals in the crumbs so you don't get any in the frosting. I let the crumb coat dry about 30 mintues and then apply the frosting. I use an angled spatula, which was only about $4 and produces much nicer results than a regular spatula or butter knife. And I invested in a rotating cake stand on ball bearings, which makes the icing process much easier.
I made my hubby a 5-layer ultimate chocolate cake over the weekend and it turned out magnificent (pronounced "the best cake I've ever had" by more than one person) so all this is quite fresh in my mind.
Re: proofing yeast, I've always done it in whatever bowl I was using at the time. Glass, stainless, plastic, it has never mattered.