You can get male plants, female plants and hermaphrodite (self fertile) plants, so it could be true.

Depends on your climate, they're basically a tropical plant with a bit of tolerance for cooler climates if their soil is well drained. They get root rot very quickly in wet conditions.

Don't know exactly how long they live but they're fast growing and become difficult to harvest fruit when the plant gets too tall. I find it better to put in new plants every few years, they only take about 18 months to fruit.

Roots aren't any more invasive than most other plants, I've never found them a problem.

How can I tell if the papaya is GMO or not? The tag does not say. Do I have to worry about it getting sick in orange county, Ca?

I think you have to rely on your suppler to let you know if the plant is a GMO. There's nothing in its appearance or the fruit that will give any indication. I don't know your climate but below freezing point the plant will die.