Yes, but in the veggie drawer.
I know Iris is a bulb, and you have to dig them up before your first frost, and wrap them (just the bulbs) in newspaper and then into a brown paper bag, and you store them in your basement. Has to be a cool place. If you have no basement, then store them in a crisper drawer of your refrigerator. Then you plant them again after your last frost. They will be beautiful come spring.
Many iris do have rhizomes. But some do have bulbs.
Iris do not need covering in winter.
Irises have either bulbs or rhizomes.
Iris do not have bulbs- they have a rhizome, a specialized root, and do not grow in small pots. Even one root in a 6 inch pot would not work.
You can store them in a breathable or non airtight container and keep them inside or even under the house. Just keep them from moisture and from freezing. I store mine in plastic buckets, woven baskets and paper sacks, same for my other bulb plants as well like iris, canna, calli, glads and daylilly bulbs.
Most irises have rhizomes but some have bulbs.
Iris bulbs should typically be planted one and a half feet apart but planting them in groups of three will yield a beautiful arrangement. So yes, you can plant them in small groups.
There are bearded iris, water iris, dwarf iris, Louisiana iris, and siberian iris. There is also blackberry iris.
Iris has tubers or rihizomes. The rihizomes store energy for the plant to rebloom the following year.
Most garden catalogs which sell fall planted bulbs (daffodils, tulips, etc) sell a varity called Dutch Iris (a small bulb) which comes in dark blue, light blue, yellow and white. They are also available in most hardware stores in the fall (bag of 20 or so for $9.95). You can search for "bearded Iris" on the internet and find several reputable companies selling the larger, and more showy bearded iris, which bloom in summer i/o spring. They grow from rhizomes and not bulbs. There are several white cultivars available.
You cannot grow Irises in an Aerogarden because they are bulbs or rhizome based, not seed.