Can immigrants visa holder enter the USA five days to the expiring date on the visa

As long as she has a valid visa, she can come in.

Can I put separated in my citizenship process ? Is asking for my marital status

You will have to have your divorce finalized. Or just put "married".

Can the sponsor process take place after I accept the job offer and start working for the company?

You can accept employment only if you are in a status allowing that. Consult with an attorney.

Does what I do it is mistake? They will ask me to file 325a?

Do not worry. It is not a big deal. If USCIS officers sees a mistake, he/she will reach out to you.

Should a non-relative sign the "affidavit of support" for a foreigner applying for a student visa?We have F1 interview concerns.

You need to consult with an attorney. You cannot expect a reliable legal advice from this forum.

Good question. Right now, you will choose WHITE. There is a strong advocacy in making it its own race, but so far, it has not happened.

How do I select one out of two H-1B COS petitions on 1st October if both get picked up in lottery ?

It will be cancelled automatically by you not working for them.

I want to immigrate to US, but I have been an F1 for more than 5 years. How should I fill out my immigration status for "tax"?

It is a question for an accountant/CPA.

I'm going to change my job so would like to know the pros/cons and what I can do and can't do with my H1B and EAD.

If you GC is denied, you will be out of status, unless new job offers H1B as well.

Will the I-130 be sufficient to file their I-485 or do we have to file a new I-130.

I think you will need to start all over again, unless you submitted I 130s when you were a green card holder and they were not used for immigrant...