Can't they find the next available slot for oath in the system and print the oath letter on the spot? You are not asking him to put you ahead of others. Sometimes we have to wonder whether they are thinking properly?
From the date they send you oath letter, you should prepare to expect it willl be a month time for your oath date. I doubt you get Dec 15th date. Schedule infopass again if you didn't receive oath letter in one or two weeks.
If you want to prepare for emergency travel before you become citizen, better option is (as Columbus is under NY Indian embassy jurisdiction), either you can drive or fly to embassy to apply for new passport in morning and get it on same day. Check the web site. You can mail, but it takes time.
The moment you take oath, you are American and not Indian and you cannot use Indian passport. You must get US passport and Indian visa.
1) Once you know the oath date, call the automated system and schedule earliest morning appointment the next day (depends how soon you want US passport). You can schedule at any one of the passport agencies. But you have to drive or fly for the appointment. If you give the application in morning, before afternoon you will get US passport.
2) Next step is to get Indian visa. OCI visa is best option, but it will take 3 months. My suggestion is apply for visitor visa (costs $170 for 10 year multi entry visa) and then or at same time apply for OCI visa. You have to goto NY Indian visa outsourcing agency and schedule morning appointment. You can get visitor visa on same day. This way you will be ready to travel within two days of becoming US citizen.
Otherwise, if you mail the applications, it can be a month to get both US passport and Indian visa (for OCI visa, add another 2 motnhs). This choice is uneasy one, as you cannot travel within a day notice. Also all your original documents get struck in mail or at embassy. Though rare, then there is fear of losing original documents in the mail.
If you go personally, you have to bear travel expenses and lose two working days (depend on method of travel).
The quickest way to prepare for travel is, get passport appointment in one of the agencies in or near to NY city (example New York, Philadelphia, Norwalk, Boston), get the US passport by afternoon, stay the night nearby, and next day morning goto Indian visa outsourcing agency in New York at 57th street and
1st Avenue (Indian embassy outsourced to private agency for visa applications), submit the application, collect the visitor visa by evening. If you get passport by afternoon, you can also give visa application same day instead of next day morning. They accept applications before 4PM, but you collect visa next day evening only.
This is quickest method and within two days, you get both passport and visa and ready to travel.
Make sure you have all filled applications and necessary documents and you have appoinments. Check websites.