Is it illegal for an immigrant with an expiring visa to have an affair with a married american?

Sorry, this isn't an immigration question ... even if a non US citizen is involved in your question.

Visitor Visa to Canada

This is not a Canadian Immigration law Blog. Go here and search for lawyers in Canada: www.ailalawyer.com

My wife and child are both U.S citizens they live in the Sates and I live in Mexico. What can we do to be together asap.

I agree with the other lawyer .. an I-130, with the help of an attorney may be just the 'ticket'.

My H1 visa approved on May 2012 but not stamped. I have to travel to US on L1 during August. Will there be any problem at POE ?

It looks OK, the way you describe it ... you are keeping the H on 'hold' until October and I assume there was no change of status involved with the...

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Attorney Ferrari is correct ... they will verify your relationship ... and possibly re-verify that your spouse is still eligible for the F-1 ......

Is it required to attach cashier's cheque or ordinary cheque for filing i751 petition?

Either one. Read the instructions closely ... or better yet, hire an attorney to help you ... we take payments so cost shouldn't be an issue.

In this situation, can I still continue to stay beyond 09/23 (the day my I-94 is expiring) or will I've to leave the country.

Mr. Ferrari is correct ... this is very complex and you had best talk to an attorney as-soon-as-possible.

Apllied I-485 got EAD/AP, But got NOID for I-140, upon sending request I-40 revoked based on ability to Pay issue.

This is a repeat question. Mr. Dixler is correct .. it is possible that her AP is now invalid. What does your lawyer say? If you don't...

TPS question

I agree with the other lawyers ... it might not be wise to travel before you meet in-person with a lawyer.

I want to petition my mother, I am a US citizen but currently I live abroad

You can start the process now ... but need to return before, or at the same time, as it is completed. Also, you didn't tell us if you are a US...