I-765 Which case am I applying for?

As my colleagues note you are applying for employment not renewal.

I am doing a cancellation of removal hearing. if I lose can the judge still give me voluntary departure.

Yes it is possible if you are eligible.

My case is on appeal due to the denial to remove condition on my green card while married to a citizen, I did file for a waiver

I agree with my colleagues speak with an immigration attorney directly.

I agree with my colleagues, if the first marriage was not ended then she may not have been free to marry you and you may be in a situation where...

Your employer may do the visa petition for you. The question of adjustment is not a clear. You may be eligible to adjust if you are able to obtain...

H-4 EAD

It is possible you will only receive EAD for the actual time the H-4 is presently valid.

Interview date has been changed by the embassy

If the consulate rescheduled the date that is the date.

ITIN for a person with a deportation trial pending

To be eligible to be employed in the US he needs Employment authorization from DHS. with the EAD he may seek a SS card.

The time determination is up the Judge and the judge's docket. Also there is no certainty the IJ will close the removal proceeding.

I am on H1B and working a full time job, I want to increase my income by working a part timer, Can I work on 1099 or I need to

You may have a second H-1B employer by having the second employer file for you but you only may be employed for the approved H1B employer.