Can my daughter be US citizen if she has married an American citizen has no criminal records?

Your son-in-law can file an immigrant petition for his wife any time, regardless of the length of time she spent in the U.S. without legal status. Usually, falling out of status makes it very difficult, if at all possible, to adjust status after an immigrant petition gets approved. The law, however, makes an exception for spouses of U.S. citizens: an alien who entered the U.S. legally can adjust status (i.e. receive a green card) on the basis of an approved immigrant petition filed by the U.S. citizen spouse, no matter how much time the alien was in the U.S. without legal status. Your daughter and her husband would have to file a packet of several forms with USCIS: Form I-130; Form I-485; Form I-864; Form G-325 for each of them; Form I-765; and Form I-131. All these forms and instructions for each of them can be downloaded from uscis.gov/forms; carefully following the instructions, your daughter and son-in-law should be able to prepare the package. They will need about $1500 for filing fees. It appears from your description of the situation that they have rather small income. Your son-in-law will have to file Form I-864 Affidavit of Support showing income no less than $29,437 ($34,462 after the birth of the third child). If he does not make that much, he would have to file Form I-864 anyway AND find someone to be your daughter's co-sponsor. Any U.S. citizen or permanent resident can be a co-sponsor (there are no kinship requirements) if he/she can independently show sufficient income or assets. "Independently" means that co-sponsor's income must be counted separately, without adding the income of your son-in-law. The income guidelines are at http://www.uscis.gov/files/form/i-864p.pdf To determine which guideline applies, count the co-sponsor's own family plus 1. If the paperwork will be done right, the rest should not present any problems.

As long as she entered the US lawfully and can prove that lawful entry, she can apply for a green card on the basis of bona fide marriage to a US citizen. She cannot just skip over to citizenship. She will first need to be approved for a green card and once she has a green card for 3 years, she can apply for US citizenship.

Your son-in-law needs to petition the USCIS on behalf of your wife. If no other problems exist, his income for affidavit of support, for 4, needs to be around $30K/year to qualify. If he has some savings, that would help also. He also needs to be in good standing and filed taxes in the last three years. If he has problems with petitioning, he needs to retain an immigration attorney. It should not be very expensive.

If your daughter is married to a US citizen and she is currently in the US, she is eligible to file for Green Card based on a marriage to a US citizen.

Your daughter will have follow the process in filing an application for a green card and her husband will have to sponsor her. They should talk with an Immigration Attorney who can help them with the process. Once she gets a green card she can file for citizenship after she has had a green card for the required period of time.

Your daughter will be fine. It is currently taking 3 months from start to finish to get a green card. As long as she last entered the country legally (even if she overstayed), she can apply for a green card through her husband. In fact, there is no penalty for the overstay.

Assuming your daughter entered the country with inspection, your son-in-law can petition for your daughter and she can apply for adjustment of status concurrently to become a lawful permanent resident. The petition is filed on form I-130 and adjustment of status is filed on form I-485. The filing fees will cost a total of $1,490.

Probably if your daughter came to US legally with inspection. If they live in Michigan, I can give then a consultation for a nominal fee.