They are annuals. Ammi majus has white flowers, according to Armitage not much different than Queen Anne's Lace. Ammi visnaga has greenish flowers. You can get more than one cut from a stem, in my limited experience. I found that Ammi visnaga needed support, so I'm not sure you'd want to use self-sown plants. Setting out plants so you can use flower netting woulkd work better.

Ammi majus will self-sow like mad, although I start new plants every year for the reason Annebert mentioned. I use some of it while it's actually blooming, but I find that after the flowers shatter the green umbel structures make an even better filler until the seeds ripen.