Can an error about country of residence (not changeability) when filling DV entry form disqualify me?

No, country of residence does not determine eligibility, country of birth does.

After I-485 Adjustment of status filing and finger printing, can I take up a new job, before I receive EAD (I-765) approval?

No, you have to wait for work authorization to be actually granted before you can work.

What are my options?

If you are an American citizen, you can file a petition for your brother but you are correct, he would have to await his priority date and that is...

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I have a valid permanent resident card, but my employment authorization card expired, can I not work anymore?

You do not need an employment authorization card ifyou are a permanent resident. Your permanent resident card is enough.

Just removed the conditions on my green card

You will retain the date of residence from when you received your conditional residence.

How can an illegal immigrant fight for visitation rights?

He should be entitled to visitation but he should consult with a family law attorney as this is not an immigration question.

Will a divorce cause me any problem like deportation?

If you never applied for adjustment because she would not submit an I-864 affidavit of support, you are in the U.S. without status and are subject...

I would like to apply for US Citizenship. Where do I start?

Check USCIS website and make sure you qualify. Complete and submit N-400. You should also consider consulting an immigration attorney.

Citizen application ask total trips or days spend outside U.S in 5 years? I said no, is problem to travel after filing?13yr here

You should be fine but remember that you will have to do biometrics and may receive notice while you are away so hopefully your trip will be short....

US visitor 10 year visa and conducting business meetings, business seminars etc.

You may attend business meetings, seminars and training, however, teaching people in your field of expertise via seminars may not be within the...