I have never tried starting flowers in an Aerogarden, but most any seed should germinate there and once it gets some growth , it can then be transplanted outside.
One of my friends on the AG forum is growing melons in an Aerogarden!! Looks like a lot of trouble to me, but I admire his experiments. I doubt I will ever try anything like this.
Marigolds! That's another one. They are so tough. It's hard to neglect them enough outdoors to kill them.
Even the tomatoes and peppers don't usually require pollinating, as the flowers usually pollinate themselves prior to opening. If you do your own hybridization of peppers or tomatoes, you have to remove the stamens prior to the flower opening. Vibration helps ensure that pollination takes place but it is not usually needed, and, as @Beth Gallagher said, leafy plants don't need it that are harvested for such. Beans, peas, and the Nightshades, such as tomatoes, peppers, and eggplants pollinate themselves, but most other plants do not. Cucumbers, squash and such require pollination unless they are Parthenocarpic and produce fruit without pollination. The fruits are then seedless as well. Beth does amazing things with her Aerogardens!
That's true. But outdoor plants have the wind, bees and insects, etc. that help shake the pollen loose in self-pollinators. The oscillating fan or manually shaking the branch is to help with pollen release to set more fruit on indoor gardens. If an aerogardener notices a lot of falling blooms and not much fruit, they should up their game on pollination assist.
That is true. We just shake our greenhouse plants by hand as we walk by. We have fans too, but they only move the plants that are close to them.