I agree. You are accumulating unlawful presence under the law after the I-94 expires. There is no grace period. "Grace periods" occur when immigrant employees are laid off and are given time to file a change of status, but even that area of the law is murky.
I agree with my colleague. Remain patient. I understand that some have already received their work permit and DACA approvals - there is no rhyme or reason why yours is taking this long, except that it is bureacracy and that USCIS did not have enough officers to adjudicate the applications submitted.
I agree with my colleagues and would add that whether she can adjust status depends if she entered with a visa. If she did enter with a visa, you have a situation that is relatively easy to solve. If she did not, then she would have to leave the country to obtain her immigrant visa as the stepdaughter of your US citizen wife. AND it would be better if she left before she was halfway to turning 19 years of age. I am not certain that a pending for DACA would prevent unlawful presence from...
I would contact an immigration attorney. There are a few facts that I do not know about your case. (Number of entries, lengths of stay, why you applied for immigrant visa rather than adjustment of status, any criminal record, etc.). I also do not know why he would be in administrative processing.
This conviction should have been disclosed with the original adjustment of status application nearly two years ago, and the appropriate certified criminal dispositions should have been submitted with that application. I would advise you to contact an immigration attorney regarding this process, if it was not disclosed.
The short answer is no, you cannot at this time. If you marry your girlfriend, she can petition for you, but you will have to wait a few years to receive your green card. Once the visa is available, you may be able to get your greencard, but it depends on your background (immigration and criminal). The process is complicated, and I highly recommend you contact an immigration attorney.
I would add that you should consult with an attorney to discuss all your options, i.e. if you get married in the U.K., if you get married when she is visiting you here in the states, if you file for a fiancee visa, etc. I would be more than happy to meet with you, since I am relatively close to you with my Charlotte office. My consultation is free. My office number is 704-577-0568.
Please ask your attorney what they are doing to terminate your removal proceedings. Whether it is terminated depends on whether you are eligible for adjustment of status - and your attorney should ask opposing counsel (Office of Chief Counsel) to join a motion to terminate proceedings. Once they approve, they send it forward to the court and the Immigration Judge approves.
You can petition for your parents when you turn twenty-one years of age. However, this does not mean they can obtain their lawful permanent resident status. Whether they can adjust status (i.e. get their greencard) in the United States depends on their immigration and criminal history. For instance, whether they entered with a visa or illegally makes a big difference whether they can stay and get their greencard. My hope is that there will be immigration reform that helps your parents...