If it were me, I would probably wait until they bloom to move them, if you are really hoping to have blooms this year. I move my bulbs all times of the year, but if you're going to be really upset if they decide not to bloom, then it's better to wait. :) Just my two cents.

Oh and I think most bulbs like sun, but I'm sure there's a shade loving bulb out there too. Are hostas considered a bulb? I'm not sure but they love shade! Lol* I bet someone here will come up with something. You are right though, you can plant your tulips under trees because they will be all done by the time your trees get their leaves. Good luck! :)

1. Like you said, it's ok to plant early-blooming bulbs under decidious trees, since they don't leaf out until later. Yes, the bulbs in full sun are probably a bit more floriferous, since the foliage gets a chance to collect more energy for next year's flowers, but the ones under trees do just fine. I don't really pay a lot of attention to sun/shade requirements when I plant bulbs, and I've never had any issues.

2. If you dig the hole first, then plant quickly without disturbing the soil around the roots, your containerized bulbs will likely do fine. Be sure to water them thoroughly the day before transplanting. If you're really worried, you could sink the whole pot into the ground and then dig and replant later after the foliage has ripened.

Good luck!