To reenter the United States after any departure where your student visa has expired, you will need a valid visa. First, if you are a full-time student and have not violated your status, you should not have a problem getting a student visa. You will need to either return to your country to get another visa or, ask your international student advisor to look into whether the US Embassy in Canada will renew your student visa. Do not leave the country unless you have a visa to reenter.
Disorderly conduct is not an inadmissible or a removable offense. Keep doing what you've been doing and be honest if asked whether you've ever been arrested. This issue will come up one more time when you apply for naturalization.
If the foreign citizen does not have a green card, he/she will eventually be deported. If the foreign citizen has a green card, there are several ways they can fight to stay depending on the facts of the case.
Physical presence is not required for applicants grandfathered before January 14, 1998. For these petitions and those filed before this date, no physical presence is required. Physcial presence is only required for beneficiaries who filed after January 14, 1998 but before April 30, 2001.
The adjustment application will be adjudicated notwithstanding the death of the petitioner under 204(l). No reinstatement is required unless the beneficiary is outside the country.
The beneficiary is...
First, if you don't have legal status you are removable with or without the DUIs.
Secondly, if you find a way to legalize your status you may encounter problems because your multiple DUIs may render you inadmissible under the physical or mental disorder grounds.
You need a lot more documents than a driver's license. What else do you have to prove that you are sharing a life and a home together? What documents do you have to show that you entered into this marriage to establish a life together?
You must do biometrics before you depart the US. Your option is to return to do the biometrics, get a document from the US Embassy for aircraft embarkation or, hopefully, you have a temporary stamp as evidence of lawful permanent residence.