It sounds like yes- based on the requirements announced by DHS last week, but as of this morning they still have not come out with all of the criteria, so you have to stay tuned to hear something in the next few days.
The removal order will have to be reopened first before your husband is eligible to adjust his status even with an approved I-485. Currently the removal order prohibits him from being granted any legal status so he will have to deal with that first. He should contact a good removal attorney to talk about his options. I recommend Leslie Diaz at 404-935-0044. Good luck!
They will probably not refuse your entry but will take a closer look at that when you apply for citizenship because that may cause a problem. Consult a lawyer about the specifics of your case. Better safe than sorry.
Yes, as long as the L-1B maintains valid status the L-2 can travel and will need to obtain a stamp through 12/2013 (will need to present proof to consulate that L-1B is maintaining status).
L-1 cannot sponsor parents to come here, only spouses and minor children (under 21). Parents will need their own work visas or visitor visas to be admitted.
A prior B1/B2 denial will most likely affect a new F1 application because you are required to prove you will return to India when the F1 Visa term is finished. If you were previously denied it means that you were not able to previously prove that you will go back to India at the terms end. Unless your situation changed and you can prove strong ties it is likely that your visa will not be approved. However, you should consult with a good immigration lawyer to see if you have a good chance or not...
You can apply for the U visa as long as the law enforcement agency completes their supplement even if the case is still ongoing. As long as you cooperated with them and they are willing to certify this you should be eligible. You should contact a good attorney to help you with this.