Is there any recourse to a Legal resident who violated Visa status in the 1990's via a drug charge (not traffic) from deport?

Contact an immigration attorney directly. There may be a few defenses get started as soon as possible. You may contact one through this website.

If someone was deported due to dwi could they apply for a pardon if parent fell ill in the states even if just temporary?

A DWI alone is not a removal gerund. More information is needed. Speak with an immigration attorney directly.

Can I have a one way ticket as an international student studying outside the US?

Not a requirement but it will be very helpful; in obtaining a visa if you have a round trip ticket.

Only if the US citizen is convicted under the Adam Walsh Act does it harm a petition.

I'd like to know if I can reopen a criminal case ( grand theft 3rd degree )

It may be possible. Speak with a criminal defense lawyer as you need a basis to reeopen.

If you are an immigrant you have papers under the INA./ if you are an intended immigrant and do not have papers see an immigration attorney as...

Can a friend with her citizenship adopt and file for my daughter?

The adoption and subsequent immigration questions need to discussed with an attorney that handles adoptions and another attorney that handles...

An I-130 may be ended for lack of prosecution or in others words for failure to act.

Will my criminal record bar me from K-1 fiancee visa I-129. I am the petitioner and finacee(in South Korea) is the beneficiary.

Your listed background does not disqualify you as a petitioner.

Had H1 before grad school, now on F1. Will I have to go through the lottery process next year to get new H1?

More detail is needed such as were in a cap subject H-1B? When did your H-1B end? Speak with your employer's immigration attorney.