So can i still fixs my papers with out him

I recommend you meet with an attorney. You seem to qualify for DACA. You may qualify for other categories.

Which law was in place in 1987 with regard to N-600? Am I eligible if my citizen parent had joint and legal custody??

You may review the chart: http://www.ilrc.org/files/documents/natz_chart-c-2015_3-4.ak_.pdf

Can I file my petition to USCIS by mentioning misspelt names in 'Other Names' or do I need to revise the original documents

We recommend you have the birth and marriage certificates corrected. listing as 'other names' will not apply to this issue.

How can I fix my parents residence status, they are currently immigrants? I am the oldest of five so my siblings depend on them.

Depending upon your status as a US citizen and whether your parents entered EWI or Overstayed and their criminal record, among other things, you...

Is it possible for me to get the same I94 number so that I can start working for the new employer without Stamping outside USA?

With the other attorney's points in mind. You may begin employment upon a new employer's receipt of their H1B change of employer petition.

Traffic tickets affect my citizenship application processing?

A single ticket with 2 points should not affect your citizenship unless it represents a disregard for the law.

Job title (LCA) and actual job

The attorney should guide the employer to demonstrate the correlation between your specialized education and the specialty sales occupation.

Your job title should be on the H1B petition, company letter, and LCA. You are required by law to be provided a copy of the LCA.

Why trading stocks is permissible and driving Uber/Lyft is not for H1B visa holders?

Deriving income from passively owning stocks would be permitted. Actively driving for Uber is not permitted. An active day trader is not permitted....

Can a Paralegal do that? Is a Paralegal someone that an individual can give power of attorney or authorization to represent us ?

A paralegal cannot represent you before the court. You might contact a law clinic or legal aid with a deportation practice.