OPT MTR and H1B application at the same time

You are probably already out of status. Consult with an attorney before listening to the Student Advisor.

That could be viewed as a material misrepresentation if it goes uncorrected.

Can I file I-601 myself without a lawyer ?

It sounds like you have already answered your own question.

Can I start LLC while on H1-B and open business checking account for the LLC with my SSN and address?

Your visa status is tied to your H-1B employer. Passive investing outside of that relationship is permitted, however, employment is prohibited.

I just got my green card through work. I have heard there is a six month waiting period before which I can't leave this job.

There is no such rule in the US immigration law.

Travel on H4 with approved H1B and before H1B start date. Do i need an amendment to start my employment?

You need to consult with the attorney that filed these petitions on your behalf. Readmission on the H-4 means that your status is H-4 not H-1B.

H1-B marrying a F1 student

He is not required to change his status to H-4 after the marriage.

H1B worker want to apply Green Card with girlfriend's (Green Card) sponsorship. But I have married status in US Embassy.

You already have a problem with immigration fraud. Consult with an attorney in confidence.

AILA is a very highly reputable organization, whose members include some of the most experienced and knowledgeable immigration attorneys in the World.

H1B Transfer and Start at the new employer after a gap of few days ?

You need to avoid a lapse of status, so the sooner after filing that you commence work with the new employer, the less likely you are to have...