It is very unlikely, however, you should consult with an immigration attorney to review the conviction records and make a complete assessment for you.
If there is an employer willing to petition for her and she has a proper credentials. It may be possible to obtain a visa based on employment.
If you are not ready to be married, but would like to marry within the next 6 to 12 months you may petition for your fiancée using a fiancée visa. She should be permitted to come to the united states,within about 5 to 7 months. When she arrives in United States you will need to be married within 90 days.
A divorce does not impact citizenship nor does a divorce necessarily impact the resident status (green card). The divorce would have impact only if there is evidence in the divorce that calls into question if the marriage was for the purpose of obtaining the resident card. You may want to have a consultation with an immigration attorney before proceeding to review the circumstances of your marriage and subsequent divorce.
ICE cannot remove or deport you without a decision from the immigration judge. You are permitted to represent yourself at a hearing but you would be better served by having immigration counsel represent you.
Generally United States citizens and their United States citizen offspring are eligible for benefits. Their receiving benefits should have no impact on your removal of condition application or your citizenship application.
It depends on the priority date which in this type of application is usually the day you filed it. CIS approves the visa petition and it is sent to the national visa center until the priority date is reach
If you wife is eligible for student visa status that is fine. An issue you may face among others is to be eligible for student status she must have a 'non-immigrant intent' that is an intent to remain in the US temporarily. To be a resident she must have immigrant 'intent' that is the intent to remain in the US permanentlt
Generally if you are a US citizen or permanent resident of the US you may petition for your spouse. However, every matter is somewhat unique and you need to contact an attorney directly for an assessment and fee quote. You may contact an attorney directly through the AVVO site.