"The baby falls in the park."
Translation:La bebo falas en la parko.
You're correct about "bebo" being the subject.
It's not "parkon" because it's not the object (recipient) of the action of the verb. "fali" is not transitive. Also, "la parko" is the object of the preposition "en" and objects of prepositions only take the accusative when there's movement involved.
La bebo falas en la parko: The baby falls in the park (The baby, who is in the park, falls).
La bebo falas en la parkon: The baby falls into the park (perhaps skydiving from above).
I am looking for an Esperanto pen friend. I learnt Esperanto out of a text book so although i can translate into and out of Esperanto text reasonably well my conversational Esperanto is appalling. At conferences people speak so fast I am lucky to understand one word in ten. Anyone out there interested in taking me on ? By email at first and then recorded voice messages and maybe telephone calls?