Platz is, in general, the free space you have to sit or move. So if they translate it as "room", they think of the free room to feel comfortable. This sentence seems good for cramped spaces like on the back seat of a car or in a theater to assure your neighbour that you still feel comfortable.
Yard or square are a different meaning of the word Platz. It translates as the free (public) space between buildings. It often has been given names like "Ernst-Reuter-Platz" or something like that.
This sentence is more about the personal space you have, so yard was correctly rated as wrong.
Is there any way I could use Raum in this sentence? I remember reading in the House lesson that Zimmer is room as a room in a house and Raum is room in the general sense of space. Am i missing something? Does Raum refer to an indoor/closed/different “space” from Platz?
The way i understand it is that platz is elbow room, but after some research, 'raum' is a bit bigger, or at least often used as bigger, than the house lesson lets on. Think Nazi "Lebensraum", the place where the Aryans would reside. Or, less extreme (extremity sticks, though), "Sprachraum," a place where the same parent language is spoken, i.e. Germany, Austria, Switzerland is the German Sprachraum. Big place. Platz in this sentence, little space.
"I have enough spots" would be "Ich habe genug Plätze" in the sense of already knowing enough spots to visit so you don't need any more suggestions.
"Ich habe genug Platz" on the other hand may be the answer if you and a friend are using the same tiny table, he is occupying more of the table and asks you if you need more "room". -> "Nein, ich habe genug Platz."
"the cemetery plot" would translate to "die Grabstelle" consisting of "das Grab" (=the grave) + "die Stelle" (=the place, the position)
"an Ort und Stelle" = "on the spot"