Does illegal stay in another country effect the Immigrant petition of spouse?

You need to consult a Mexican attorney regarding this issue. Generally, immigration violations in third countries has nothing to do with the case...

Depends on the Office processing your application, but normally 30-60 days.

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Path forward from L1B to GC

This is way too general question to be answered. Normally, your petitioning employer would start a PERM process (labor certification) in advance, ...

Withdrawing request for admission is not the same as removal and does not bear consequences of deportation. However, you need to consult a lawyer...

Can someone petition for his wife from abroad and complete the whole process without coming to US?

Yes, if he can show firm intent to resettle in the US.

There are no set attorney's fees and the cost may vary significantly depending on attorney's experience and geographic location of the office.

For EB-2 classification, is it necessary that I should have at least one year of experience after obtaining my master degree?

It is hard to tell what your employer's assessment is based on. Generally, EB2 process does not require any specific years of experience if you...

Applying Deferred Action for Childhood Arrivals after expired F1/OPT visa.

If you were in the U.S. in legal status (meaning, as a student or on OPT) on the day the DACA was enacted, you do not qualify.

Do I have derivative citizenship ?

If you were not a resident at the time your father naturalized, you did not derive your citizenship automatically.

Is he able to enter?

If he has a proof of his timely departure, there should not be any issues. He did not accumulate enough unlawful presence to trig the bar.