These are all excellent questions that should be addressed to the immigration attorney who prepared and filed your employment-based AOS. He or she has been paid for that.
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
It's a letter from the consulate/embassy to the airline to let you travel to the U.S. They often refuse to give it. They will not let you to the I-90 if you are out of the U.S. Basically you abandoned your adjustment application when you left the U.S. for 9 months and past the date allowed for you to return and in my experience, you will need a new visa to immigrate, or can try to file an I-824 [which may take much longer than a new I-130].
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
You can travel to the US using a transportation letter. A form I-90 is an application for a replacement green card.
Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.