I need to travel while i'm pending asylum, can i travel and come back safe?

It is best to consult with an attorney in private for assistance with such travel.

How much time does it takes for them to make a decision and respond to a case like ours?

If the officer informed you of 3 months for a decision, I would wait 3-6 months before contacting further.

Immmigration status

I agree with my colleague - you would be an “Asylum pending”

RE submit the passport with US immigrant visa for spell correction in given name,how they put that in Administrative processing

Administrative processing is not uncommon and can take several months to complete. You can contact the Embassy for a status update if you haven’t...

Charges dismissed, never arrested, will this effect employment?

It is best to speak to your attorney regarding any consequences of the charges.

May I leave USA for two months in August and come back in October if my two year Green Card expires in November?

Yes as long as you reenter before your I751 expires. You can also acquire a I551 stamp by scheduling an Infopass appointment before departing.

You can provide the report you filed with USPS that it was not delivered. Refer to the RFE instructions for guidance.

If you are currently in the US you can remain until your I94 expires and are free to travel domestically while here.

You can sign the certificate anywhere since it is not after your ceremony anyways.

Can I find another Sponsor besides the one in the DS 260 before interview

Yes you can obtain a second cosignor for the affidavit of support requirements.