Can an employer file I-129 for me while my F-2 is pending?

The H1b may be authorized, however, to change status from F2to H1b you need to be in status..

Is delay in H4EAD processing related to pending H1B Amendment?

H4 Ead is based on your spouse's H4 not on an amended h1b

Am I eligible for e-filing of I-765? And Do I need to pay for I-765?

Regular mail with delivery confirmation is just as good or better than filing as my colleagues have mentioned.

Please help me understand when my unlawful presence starts ? How long is my ban ?

You begin accumulation of time counting toward unlawful presence when your status ended. 1 year of time out of status results uIn an unlawful...

Being a Green Card holder, what options available to bring an Indian citizen spouse to the USA? We aren't married, but planning.

As a resident a petition may be filed but resident status is not available until the priority date is reached or the resident becomes a U.S....

Yes you may travel. The EAD is not forward so make sure it is picked up.

My friend is from Jamaica and he got married to a US citizen can he divorce her and remarrie another us citizen

Divorce and remarriage is possible. More information is needed to assess if it will impact immigration status.

Filed I130/I485 and 485status says "On July XX, 2015, we ordered your new card for Receipt Number MSCXX. Is green card approved?

Yes the application has been approved. Congratulations.

I am currently on H1B Visa. I would like to know if I need to restart my green card processing if I join my previous employer.

You may be able to port the priority date but will likely require a new LC. Speak to the employers immigrati attorney.

Getting visa for wife

You are not likely to be successful in obtaining a B visa for her. Consider the consulates advice and consider working with an immigration attorney...