I am 18 years old, and in the next week my parents will proceed with the Permanent Residency procedure according to their L-1 Status. I wish to leave the U.S. to study and work in Mexico. My question is, once the residency fees are paid and the Permanent Residency is in process, can I leave the country, as a dependent, and if so, are there any negative effects on my status?

Once I leave the country is my process 'abandoned'? Do I need to stay for any specific reason such as an interview towards the end of the legal procedure or as a dependent can I just wait abroad and let my parents handle everything?

If you file as a dependent along with your parents, you will need an advance parole travel document to ensure your return to the US without abandoning the 485 application.

I've read an advanced parole travel document takes months to process, is this true?
If I were to leave the United States during the 485 application, how would I be impeded? Is there a document I have to sign, an interview I have to attend? I doubt they can immediately find out I left the country and sign me off as 'abandoning' the application.
Is there a need for me to be physically present?

Agree with NYcityboy...

You will need an advance parole travel document.. good luck.

I've read an advanced parole travel document takes months to process, is this true?
If i were to leave the United States during the 485 application, how would i be impeded? Is there a document i have to sign, an interview i have to attend? I doubt they can immediatly find out i left the country and sign me off as 'abandoning' the application.
Is there a need for me to be physically present?

The AP is usually issued about 90 days from date of filing. You wouldn't be stopped from leaving, just from re-entering. They don't need to know if you left the US, as you need attest to that and will need to testify to that if you are interviewed. They will know how and when you entered with the visa that you use.

I advise you to consult with a certified specialist in immigration and they can help you with a timeline. There are ways to expedite the AP issuance. Good luck in school! :)