1. No, you could enter in advance parole, but it would be best to obtain a new visa.
2. Your wife and children would be out of status. This may not be an issue if they have each filed a Form I-485.
3. Speak to your employer's attorney to plan how to best proceed. You do not need to extend your L-1A if you have an application for adjustment of status pending.
Answered on Feb 11th, 2016 at 4:27 PM