J1 Visa

She might be overqualified for a J1 you should try H1B or L1. Consult with an immigration attorney in private. All the best.

We're common law spouses filing for a B1/B2 extension. Should we file one application per person or file one for the both of us?

Separate applications for each one of you. All the best.

Is applying for DV lottery for green card can cause a problem for applying to another visa outside the US?

Yes, and no. You will only face difficulties if you entry is picked so you do not have to worry much about it at this point. All the best.

What Do I do????

I agree, use the link below to set up an appointment. All the best. https://infopass.uscis.gov/

Yes it is possible to apply for COS, regarding whether or not it is legal to break the J1 you should look at the employment contract and act...

Immigration

Sorry about your loss, you may be able to come back in because this was an emergency and not something that was planned. Talk to an immigration...

How long will it take to typically process conversion to a green card using EB2 from the time the employer completes petition?

You can check the processing times from this link - https://egov.uscis.gov/cris/processTimesDisplayInit.do

Next time you apply for passport renewal you can change the name by providing proof. Also keep in mind to use one name for all of the applications...

Citizenship Denial: In regards to demonstrating 5 years of good moral character what day/month/year should I be counting from?

You should be counting on the last 5 years so it will include both 2010 and 2012 also. All the best.

Me and my wife file the petition for her to get residence but it taking longer than we expected

I highly doubt you can extend this unless you have very good reason to do so. You just have to wait for this process. Are you a citizen or a LPR?