I came to the us on a f1 visa to study at a non existent college then I got a job as a manager at a brewery and worked there

if you have a qualifying relative you might obtain a waiver. Marriage to a US citizen will eliminate the need of a waiver.

Do i Need to fly back or not?

Living together is evidence of a bonafide relationship

How can I claim 2 months of pending salary from previous h1b employer?

if you are owed wages you may contact the Dept of Labor Wage & Hour division.

You may have a VAWA claim if you can substantiate your claim and innocence.

If I travel outside the states while my N-400 is in process. Do I have to submit any further documentations about my trips ?

You may file as soon as you are eligible. Short trips would need to be updated at the interview when the officer reviews your passport. Each...

Is there anyway around that 5 years requirements ? and what would you recommend in this case ?

There is no way around the US 5 year residence requirement. However, you may move to the US and sponsor your child for a green card.

Do I have a year after sending off the I-693 if I did it 3 months ago or do I have 9 months?

If you go to the USCIS website you will find it is valid for 1 year from submission.

How much time does the USCIS usually take to process an employment authorization? Can I apply before entering the US?

You must be in the US to apply for employment authorization.

H1b and unemployment

Generally, applying for unemployment may evidence you are out of status. If out of status it is because of USCIS processing times. However, do not...

Am I eligible for cap exempt cos if H1b petition is withdrawn before revocation?

If an H1B cap is ultimately revoked subsequent H1B change of status will be revoked.