Im in the USA in Texas on an L1, my wife and kid L2. Can my wife leave the State/country with our daughter without my consent?

I know you have already been switched once, but this is really a family law question, not immigration. From an immigration standpoint she and your...

Do I have to withdraw I-485 because I'm out of the country?

When you ask CIS to cancel the I-485 you also ask them to send the approved I-130 to NVC and initiate consular processing.

What's my current status ?

You will not be deported but will have to wait until Aug to get a driver's license and SS card, and open a bank account.

If your spouse is not in the US, he does not have H-4 status to begin with.

Will my company pay for salary difference as signed in I-129S

The company must pay your the higher of the actual wage for that position in that location or the prevailing wage approved by DOL. So, you should...

How can i be sure that my visa still valid

Actually you have a much bigger problem unless you plan to leave and reenter using the F-1 visa.

How H4 member can travel when H1b is in progress?

Doesn't your immigration attorney know the answers to these questions? AVVO is for people who do not have attorneys.

Employment based Counselor processing for Green card

You are referring to Consular processing and it is only a few months faster and much more expensive. That step in the process is not the problem.

What is the best Visa for my mum to come to the usa from france, in order to watch my kids (under 1 year old) for a long time ?

There is no visa for your mother to do that unless you can sponsor her for a green card.

Can I stay with my spouse during visa process time

There are a lot of facts missing from the story so we cannot answer these questions. Your best option is to consult with a Board Certified...