No, only U.S. citizens 21 years or older can apply for their parents and, in some cases, they can apply for their stepparents as well.
Yes. Lawful permanent residents (green card holders) can petition for spouses by filing a form I-130 Petition for Alien Relative. Spouses in lawful status in the U.S. can apply to adjust status to lawful permanent residency when a visa becomes available.
You can apply for naturalization to become a U.S. citizen after you've had your green card for at least five years, or three years If you received the green card through marriage to a U.S. citizen and continue to be married and living together with that U.S. citizen. You must also meet several other requirements to qualify to apply for your citizenship.
The length of the process depends on several factors: if your spouse is a U.S. citizen or a green card holder; if you are in the U.S. in legal status or not; if you violated immigration laws; how you entered the country, and so forth. The same factors will apply if you are outside the United States. Because the answer to this question depends on the facts of your case, it is best to contact an experienced immigration law attorney to get an answer that is based on those facts.