1) yes, you plant in fall for spring flowers. In NC you can usually plant all through October. In fact, I have planted them in warm spells well into November and even december and still had them bloom. I don't like to plant them in September because they sometimes get tricked into coming up early, but this often happens with early blooming bulbs left in the ground and most still bloom so you probably can.
2)If the shade is under deciduous trees then early spring bulbs often get enough sunlight to produce flowers the next year, but they won't multiply as fast or flower as much as they would in full sun usually. In part shade under deciduous trees (which is almost full sun in early spring) I have daffodils, crocuses, wood hyacynths, and squill (scilla) doing well. I have had luck with some irises in part shade (though they are really rhizomes).
3)They will say on the package how far apart to plant, it depends on the bulb.
4)I never water bulbs in the winter because some can rot. If it was a really dry spring I might water, but it's almost never necessary. The daffs and crocuses can usually handle any soil, some bulbs might benefit from better soil.
5) some people like those bulb planters. In thick clay they can be hard to push down. I think a hand spade works fine, but that's me.
6)The bulbs I mentioned are all perennial in NC. Most bulbs you buy will probably bloom the first year because the energy has already been stored in the bulbs for next years flowering, but if they don't get enough light to the leaves before they die back then they may not flower again.

If you have moderate shade under evergreen trees not many bulbs would flower well but there are many other types of perennials that might brighten those spots. Good luck! -Ais.