1. Aeration is a hard issue to tack down, at least from a newbie standpoint. I classify myself in that category, by the way. I've done six batches so far, and so far I've had good yeast...promulgation? Bloom? Anyway...my yeast have always done well, in my limited estimation. I've done two methods: 1) after getting the wort down to pitching temps, vigorously sloshing the wort in the glass carboy for about two minutes, and 2) vigorously sloshing the wort and yeast shortly after pitching. I'm of the opinion that today's yeast are remarkably forgiving of newbie mistakes and can thrive even in the most difficult of circumstances. However, making a truly excellent beer probably requires you to be more helpful to your yeasts, and I've not made a truly excellent beer yet.
2. I'm assuming you're talking about priming sugar and bottling day. Normally, you put the priming sugar / boiled water solution in to the bottling bucket first, then add the transferred flat beer in, in a gentle swirling motion, being careful not to get the flat beer too aerated. And then, carefully using a stir spoon to further mix the beer / sugar mixture without too much turbulence to risk aerating the beer.
3. I haven't tried them myself, so I don't know. I prefer to err on the side of caution and don't use them.
4. It does not hurt to leave it in primary for at least three weeks, at least, with modern yeast strains. The kit instructions are trying to rush the process, so you won't be frustrated waiting so long, and also so you'll buy another kit quicker. Yeast do wonderful things if you just let them be for at least three weeks. But hydrometer tests are the ultimate decider in when a beer is done with fermentation.