Yes they can. Remember, it is against the law to marry someone for residency and not for love, even though VERY hard to prove, they do ask questions as to what type of panties does she wear, What side of bed he sleeps on, etc., etc.! However, an illegal resident can not leave the country as they will NOT be allowed in until green card is issued! Contact Immigration for application. It will run you ~$500+ for application, medical & criminal record check. If you have other questions contact me at candlefactoryco@candlefactoryco.com (RAArchie)
Yes, however marrying a U.S. citizen does not automatically confer or guarantee that said person will be granted permanent resident status or citizenship, or will not face deportation depending upon individual circumstances. For specific information...United States Citizenship and Immigration Services, http://www.uscis.gov