You will want to refer to these: https://www.duolingo.com/skill/ru/Where-is-it%3F
In particular, the prepositional case, is of interest to you. В <noun> at the beginning of this sentence, indicating that we are 'at a certain place', implies the prepositional case. So that means that you write that part of the sentence in prepositional (also known as Locative).
So that means it is both етом and парке as that is the prepositional/Locative version of the words.
I was able to guess the sentence in context, but wouldn't have been able to construct this sentence on my own. Is it парке есть the same way we structure у ___ есть to mean that the park has something? And в парке as in "in the park"? How does the sentence then get structured to в этом парке есть туалет?
It's Prepositional Case, masculine endings for the determine "this" этом and the noun "park" парке.
Парке is the object of the preposition В, and этом agrees with the case of парке.
B = "at/in" and uses Prepositional Case for location, Accusative Case when movement is involved.
There are a number of discussions at Duo dedicated to listing the Russian cases associated with various prepositions. Unfortunately, I don't have a link to those, and Duo's search engine is so bad that they are impossible to find easily.
They can be found on the internet in various places, none of which is comprehensive. For example:
Note that the same preposition can have different cases, depending on the use, often distinguished by the presence or absence of motion
If that requires a change to the Russian statement, then I would not consider 'are there restrooms' a correct translation for this sentence. It might not be the most natural way to phrase the question, I suppose, but the sentence as is would not be a good match for the translation you are suggesting then.