Can i travel to home country without receiving GC How long can i stay outside USA

Your friends/family can mail you the actual card, but you cannot stay out of the country for too long.

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Please direct me.

Are you sure he/she will not be abusing you? I think you should be careful. I also think you should speak with an attorney...

Possibly, PERM requires certain steps and notices to be done correctly. Your employer's attorney would know what to do.

Do I need to remove condition?

I am not sure how you "revived" your green card. If you were admitted as a conditional resident, you do need to remove the condition.

Can I marry a U.S. citizen? Can I fix my legal status with or without him?

You can "fix" your papers one way or another. You can get married even if you do not have "legal" papers. Just talk to an Immigration attorney....

What is the normal time to wait for the ceremony letter come in the mail.

It all depends. I would say no longer than a couple of months.

Petitioning sibling living in US

You can petition for him, of course. If he will be able to get his green card based on that petition without leaving the US, is a different story.

What is the process of paying Tax, as far International students during OPT period and US Tax Laws are concerned.

I suspect you need to pay taxes just like all US residents. Speak with the CPA or a Tax attorney.

After consulting with immigration attorney, my new employer thinks it may be risky to proceed with the H-1B petition. Why?

There might be thousands of possible issues. I suggest you simply look for another employer.

Will I do worse if I apply to appeal to the judge (case is more than 4 months in process) or any better advice? My i765 approved

I am not sure what was approved and what you need help with. However, it is time to fo and see an attorney.