It appears that you forgot that da is a preposition, and there is no object after a preposition (one of the fundamental rules of Esperanto). No worries, it took me a bit to figure that one out myself.
And I would not expect a noun multo in that location since what is needed is a describing word. So, either an adjective or an adverb. Since we are using da (= "a quantity of, etc.") to discuss spaco, an adverb seems to work best, and most clearly.
Thanks for the question, it made me think a bit, and forced me to research something which I was taking for granted (apparently with good reason.)
And yes, Okupi is normally transitive. Good call there.
What do you mean that it is normally transitive? I thought that in Esperanto a word is either transitive or intransitive, which can only be changed with -iĝ and -ig?
On vortaro.net I see an example sentence: "la libroj okupas la tutan skribotablon". So for our example I would expect: "Tiu lito okupas multan spacon". Would that be correct?
Is a maybe that multe da spaco as a whole is the object in the sentence?
Normally, but for the rule that prepositions govern the nominative. So it would still be transitive, it just won't act that way.
Your sample sentence also works, and would likely be used by Esperantists in Real Life, it just isn't the lesson we're supposed to be learning here.
And I believe that I also answered your final question in my first sentence.
Laŭ Montegue Butler; The forms onia and onin are good and logical, but not often used.
In other words, use those forms sparingly, there is usually a more regularly used workaround.
Kiam la apartamento de oni estas malgranda…
Kiam oni havas (tro) malgrandan apartamenton…