How can you find out if a person is here illegally?

Unless they are willing to tell you themselves you may not be able to know their legal status. All the best.

After successful H1B transfer,if I opt to continue wth current employer,Am I allowed?Will my current employer know abt transfer?

If the H1B "TRANSFER" is approved then you will not be able to continue with the current employer.

.

You need to read the instructions in the notice from USCIS, if it says they need a new I-864 you should do a new one with your income verification...

Do not post repeat questions. You already asked this question refer to the answer in that question.

How can I apply for his citizenship? Please advise. Or should I have a sibling adopt my nephew to file for a green card?

You need to contact an immigration attorney to help file a form for your nephew to get him US citizenship and US passport. Usually this form is...

Can I accept Permanent full time employment while on E-3 visa?

Yes you may work for the client, you can also file the LCA yourself but it is recommended that you have an attorney help you. All the best.

Can I travel in the first week of April when my H1 is filed?

It shouldn't have any problem as April is just the month for the lottery, even if your H1B is picked and approved you will not be able to work...

What can I do? Can she take care even for few days without my permission? can she get a passport for kid without my signature?

This is not an immigration question, but you should consider talking about this to a Family Law attorney. All the best.

My ex-spouse particulars are slightly diffrent. Can I change in my green card application, which was filed severla years ago.?

If the green card application is still pending you can send a letter to USCIS to fix the error. All the best.

With an approved I601A here in the USA can they reject it because she brought her son illegally to the USA at her interview?

If she has some other problems such as a criminal record or something of that kind she might get rejected, but she will not get rejected because of...