Rest assured, you can travel with just the I-797 USCIS receipt notice of your I-751, which will state that with that receipt your green card status is extended for an additional year and that travel and employemnt are authorized. You need nothing else (except a valid national passport, of course.)
Oh, and your biometrics appointment: nothing is easier. Simply take your flight ticket (or electronic reservation) with your biometrics appointment letter to the ASC any day, ask to speak to the supervisor (only!). Show them you'll be traveling and they'll take you, out of turn, that same day you go, without any problem. (I always send my clients to do that in situations similar to yours, all over the country, no one ever faced a problem or was refused.) Bon voyage!
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.
You can travel with your I-751 receipt. The fingerprint appointments are usually scheduled one month in advance, so you will have sufficient notice. In case you receive the fingerprint notice before your travel and is scheduled on a date that you are abroad, you can take it to the Application Support Center with proof of travel plans and request that they do it earlier, OR simply follow the instructions on the form on rescheduling the appointment.
This is loaded with questions, some of which may be best answered during an appointment with a competent and experienced immigration attorney. That said, you can travel on the notice of action extending your right to travel and your expired card. If you biometric fingerprint appointment takes place during your planned trip, then come in earlier with proof that you plan to travel. The USCIS will likely take your fingerprints early if you for some reason must miss the appointment. However, it is less complicated if you try to go earlier or reschedule the fingerprint appointment. Have a good trip. Good luck.
This is general information, not legal advice, and does not create an attorney client relationship.
You can travel. Make sure check with home about biometrics appointment.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.