Can I send a job letter with current pay slips to prove I meet the 125% poverty line

Yes that will comply with the I864 requirements. Good luck.

I would recommend scheduling an Infopass appointment for case processing questions and information. Good luck.

Forms required to be filed when applying for a marriage based green card.

I would recommend having a consultation to learn more or contact USCIS for instructions on filing on your own. Good luck.

Do attorney's always wait for RFE's to send evidence for K-1 visa's? Do lawyer's look forward to receiving RFE's?

I would address with your attorney but no good attorney would submit a bare bones application to await a later RFE.

Can sex offender eligible to be my sponsor to apply for visa?

Consult with Thai embassy for him visiting. But no, he can not sponsor a visa or green card for you under the Adam Walsh Act.

What is the best way for her to move to USA ? What documents do we need to produce at the time of dependent visa?

For H4 status you will need a valid marriage certificate and divorce decree. The visitor visa denial should not adversely affect the H4. Good luck.

Should I pay a fee for a I-131????

I agree with my colleagues - the I-485 filing fees include the I-131 fee.

I sponsor my dad so now can he sponser my sister next year?

Yes, once he acquires residency, he can sponsor his unmarried daughter. Good luck.

How hard would it be as a US Veteran with PTSD receiving 100% benefits, to send for my girlfriend / fiancé in Haiti.

I would recommend a consult with an experienced attorney as this request requires more in depth discussion. Good luck.

I-485 approval while I'm traveling on AP. Can I re-enter as a parolee?

Yes you can reenter, assuming the 485 is approved.