Is it legal in immigration at airport to send a pregnant woman back to her country without making a phone call or ask a doctor

Yes, this is legal though it is unclear why the doctor in your home country recommended you travel in the third trimester.

Can I legally use a one month unpaid vacation while I am in H1B?

Do other employees at you company also receive unpaid vacation?

It will violate your H-1B status to do so.

Will I benefit from TPS for Syrians in this case?

Please refer to your original posting for more information.

After two times denial history for F1 visa, how much would it be possible to get the approval for B1/B2 visa?

The B1 can also be denied for lack of social ties to Iran. http://iran.usembassy.gov/visas/niv-iranians.html

Will I qualify for TPS for Syrians?

You can learn more about the requirements here: https://www.uscis.gov/humanitarian/temporary-protected-status

Question:- 1)In this situation if I travel to India on Apr 27th will that be a impact for my h1b extension approval?

The SOW could adversely impact the case, it depends on the USCIS officer. After the documents are received, the PP clock restarts.

How long can I legally stay in USA from the date of my OPT denial.Can I stay for 30 or 60 days from denial date?

The OPT denial does not give you an extra grace period.

What are my options regarding this situation?

How did you receive the summons if you are homeless? Was it at your place of employment?

How do I go about getting an eviction? What do I need to know? How soon can I get them out?

You can go to the courthouse and obtain pamphlets about how to do these things. The court clerk may also be able to provide some information.