The issue is a difficult one given the past order(s) of removal especially. A prior order of removal will usually bar adjustment of status with limited exceptions. The criminal arrests are also a concern. He should seek the advice of a competent immigration attorney preferably who is a member of AILA. Visit http://www.aila.org/ and search for an attorney. The only other possible issue is whether the "partner" is a spouse or not. It is not clear from your question. If a spouse would be able to file a petition for alien relative at least but not clear from your question whether a live-in partner only or married. Seek advice from AILA attorney.
No attorney-client relationship is created or implied by this communication in any way. Consult a competent immigration attorney preferably one who is a member of the American Immigration Lawyers Association (AILA).
On the facts provided not likely as he could have triggered a permanent bar. My suggestion would be to first file a FOIA request to obtain a copy of his immigration file. Also get copies of the criminal convictions. Once you have this information a qualified immigration attorney will be better informed to discuss options available. If he needs assistance filing out a FOIA request my office can assist for a nominal fee. Good luck!