Is advance parole, flying to Mexico for 2 weeks to see her sick sister and returning the U.S. the best option we have?

You have been told correctly. And, this may be the best route available to her. Absent a complete amnesty which is not likely in the foreseeable...

Regarding visa, is it easier to look for a job in a european company based in the U.S. as a european citizen?

A Belgium company would make an E visa a possibility. Other visas may be available as well.

Yes, you will be out of status. Why not look for another employment. Although, out of status you are in a period of authorized stay until the end...

My question is would she be able to apply for DAPA or have any other chance of being able to come back?

Your mother not be eligible for DAPA should it be re-established.

Can I change my H1b transfer from regular process to premium process, without informing my employer his attorney?

The pending H1B transfer is the employer's petition. You may not circumvent the employer to file premium..

Extension Approval - Change of Employer before Visa Approval

If you are currently in H1B status you may change employer's within the validity dates of the current H1B status. If after the validity dates your...

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How long do I have to stay or work for my employer/petitioner EB3? I want to change employer asap. What will be the requirements

AC21 regulations provide you may change employers 180 days from the date your I-485 is filed.

M1 visa re application

The most frequent basis for such a refusal concerns the requirement that the prospective visitor or student possess a residence abroad he/she has...

Can LPR use the US property deed and filing of US tax returns instead of re-entry permit to enter the US after one year trailing

Don't leave your US home without a re-entry permit if leaving the US for one year or more.

Although, you may have only one status. A person on H1B may apply for an E-2 visa or change of status to E-2. No minimum investment is required...