There is no known timeline for when to expect one's work permit.

There is no difference traveling from Texas to California and Texas to Hawaii.

I'm sure there is no law prohibiting a person from ordering their criminal records from outside the U.S.

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You are authorized to work. You can show an employer either card you wish to show.

If your H1b is not expired it's fine. If it is expired, you need a new one to return to the U.S.

There are procedures to do international adoptions. See a lawyer.

Yes, a traffic citation is a citation. You should provide it.

The receipt notice is not an approval notice. No, you are not authorized to work until USCIS grants your application.

The rules change all the time and you should assume that you will need to leave the country to change to H1b. You might be eligible to adjust...

I am not aware of any rule against filing for TPS when you have a pending adjustment. Of course if you are granted adjustment you cannot have TPS.