You can explain the situation to the officer at time of interview and it should not be an issue at all.

Can I stay even though I 539 is pending?

Yes, you may remain while your application is pending.

Is this Unauthorized work?

You should be honest about the work but it can be waived through AOS through marriage to USC.

I 485 ,I 765, I 130 was rejected because my lawyer filed an outdated version of the I 485 i resubmitted.

Yes the receipts will be reissued once accepted.

While unauthorized employment through AOS is forgiven, it is not advisable.

Yes residing in PR counts towards permanent residency.

I filed form I130, I want to file form I1485 for my adult daughter and i am a permanent resident.

Unfortunately you must wait until the visa becomes available to be adjustment eligible.

What are the chances of being denied a green card if I worked for a year without authorization?

Unauthorized work is not a bar from adjustment of status through good faith marriage to a USC.

My conditional green card expires march 21st. I filed form i-751 in January. My concern is I did not put i-751 on the envelope.

It appears you did not file to the correct address. Consult with an attorney for guidance.

You should contact USCIS to inform them of the name change.