H1 (7th year) transfer while perm is appealed in BALCA

I would not but I do not know the details of your appeal. You should discuss this with the attorney who is handling the appeal.

Can evasion of housing contract in USA result in problems with obtaining the US visa for foreigners in the future

More information is needed to answer your question.

I am lpr. My wife is in removal proceeding. Will she be able to adjust here if the 130 gets approved and we close her court case

As my colleague point, there are many factors to consider. The adjustment of status seems unlikely given her current status and pending removal...

Employment Authorization Document (EAD) extension for L2 visa holders

You should have your attorney handle this for you. Be sure to apply for EAD at least 90 days in advance and seek extension for your spouse. If you...

Am I liable for someone on my auto policy who got into an accident in his own car? 21st Century will not answer this for me.

Based on the information you provide, it is unlikely that you will be liable unless the driver was working for you.

Travelling to Puerto Rico. What documents do I need ?

You will need an H-1B visa stamp from consulate to enter back into the United States. An approval from the USCIS or a valid I-94 will not allow you...

What are my chances of this outcome working in my favor?

This question is better suited for the family law section of this forum. I will correct the practice area.

I'm adjusting my status based on marriage to US citizen. I'm currently on F1 visa and I130 form has already been approved.

YOu seem to be having a difficult time with this. The I-130 and I-485 could have been filed at the same time based on the information you provide....

The H-4 does not limit your ability to work outside the United States. As long as you have a visa stamp and the H-1B of your spouse remains active,...

I need help related to immigration and child custody.

Your question is better suited for the family law section of this website. You should speak with and retain a local family law attorney...