Well... I'm sure that without oxygen Bettas would die quite quickly... Just like any other aerobic organism on this planet. They simply go to the surface to get their oxygen. A mechanism they've retained from their little puddle dwelling cousins in asia... They're gills are greatly reduced...
And the fact that they prefer tight/small containers is more myth than truth. They *can* live in small places because of the fact that they can breath from the surface of their water bowls, but you may notice captive bread Bettas are rather lethargic, and possibly mishappend. They are fish, and they need to excercise. Although aggressive in breeding, and do have tha pinash to fight back at other fish, Bettas are timid, adn merely need places to hide, and swim around in. So a massive tank with lots of castles and plants would be preffered by a Betta, over a tiny bowl...
On to the plants.
I had a floating plant in with my betta... As long as you keep the fish *well* fed (not over fed, baaad), it will leave them alone, barring the odd pecking here and there... I left my fishy alone for a tad bit longer than was healthy, adn he simply demolished the plant. It ripped every single leaf off of the plant, and left only small pieces of severed stem. They are carnivorous by nature, but will obviously revert to herbivory, like alot of other creatures (dogs, cats...) would without the presence of an adequate food source...