If you remain married, she can apply for citizenship after 3 years of residence in the US. However, if she's hold the green card for 5 years and has live in the US for 5 years, she can apply at that time if it is sooner than the married case.
You can apply for dual citizenship to the USA and almost any other country. Many more people than you might think hold dual citizenship. But the road to dual citizenship, with only a few exceptions, is long, twisting and full of "gotchas".
When he received his green card (permanent resident alien registration) in 1976, he was informed that he would be eligible to apply for US citizenship in 1981. He unfortunately didn't live long enough to apply.