11. Can I adjust status to legal permanent resident on L-2 visa?
Yes, you may apply for Adjustment of Status. Based on the L-1 principals adjustment of status application.You need to file Form I-485 Application to Register Permanent Residence or Adjust Status, with the USCIS.
12. Do I need to apply for Advance Parole when I have to travel abroad on L-2 visa?
No, you do not need to apply for Advance Parole if you are a valid L-2 visa holder and wish to travel internationally. This is true as long as you maintain nonimmigrant status.
13. Can I change from H-4 to L-2 status so that I can get work authorization?
Yes, if your spouse qualifies for L-1 status, you may apply for a change of status from H-4 to L-2 status and your spouse from H-1B to L-1 status. To obtain work authorization, you should submit Form I-765, Application for Employment Authorization, together with your Form I-539, Application for Change or Extension of Status.