Is it possible to go on h1b from b1/b2 applied decision pending ?

You can file cos of status if you have maintained status and seek visa if you are eligible and have maintained status

H1B extension (max out) approved only for 3 months based on approved 140 ?

Need more information to determine why extension is 3months. The immigration attorney that prepared the filing should have the information. You...

Even with a well documented filing your case may have processing delays.

H1B - bridge transfer with valid I94 and stamped VISA - need to go out of US and come back?

For specific advice talk with the immigration attorney preparing filing for employer C

You need the filing number for the approval.

Is it possible to expedite green card?

Expedite is unlikely, however, you should be permitted to attend school with your Ashlee status.

How can I sponsor a non related immigrant to the United States on a tourist visa ?

The person seeking the visitor visa files on their own merits. You cannot sponsor but You can offer room board transportation.

H1b 6th year extension based on approve 140 AC21

The immigration attorney that prepared the fling in behalf of your employer should have the details of you filing and is in the best position to...

Is there a hope to adjust a status on the individual hearing and cancel removal proceedings ?

Are you seeking cancellation of removal? More information is needed and a complete review of what been filed before responsive reply to question...

Do I have to cancel my current J-1 visa before applying for a new one?

You do not have to cancel your visa before applying for another visa.