Edison, NJ Immigration Law Firms & Lawyers

Generally, a U.S. citizen age 21 or older may apply for a parent to adjust status to become a Lawful Permanent Resident (to get a "Green Card") if that parent is in the U.S. and had entered the country lawfully and with inspection. If any of those details do not apply, then a completely different legal analysis may be required. It would be wise to engage an immigration attorney to learn all of the relevant information about your mother, including about her immigration-related history, in order to advise about immigration eligibilities, options and strategies, and to represent you and your mother in that process. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.

It would depend on the type of convictions, when they occurred and when you were deported. An experienced immigration attorney would need to review your record in detail to answer this kind of question.  

You should upgrade the I-130. I-129 was designed to expedite the process at a time that I-130s would take years. But now they are processed quickly and there is no need for I-129.