Hi Sivan, congratulations on your impending arrival!
Some hospitals will do the birth certificate for you, but only if you have a marriage libreta and if the name is on the list of names. Otherwise you need to make an appt at your local registro civil http://www.buenosaires.gob.ar/areas/registrocivil/ click on the turnos link. One of the parents needs to go along with the baby, taking the medical slip the hospital gave you with the birth details. You will need your DNI too. Ask for several extra certified copies, they are useful to have. If the name isn't on the list, it's more complicated.
For the passport, make an appt, you get the DNI done at the same time, apply for a turno here http://turnos.mininterior.gov.ar/turnosWeb/
It used to be that for a baby it had to be done only at Paseo Colon because of the special baby fingerprint equipment, maybe it's changed. You will need to take your DNI for that too and the birth certificate plus, I think, a copy.
I don't know about the permiso de viajar, I understand an escribano will do it for you. Best of luck!