"Bu" can grammatically be either an adjective modifying a noun ("bu saray"="this palace," as opposed to other palaces) or a pronoun standing in for a noun ("bu"="this," i.e. the thousandth room). The comma resolves this ambiguity.
"Bu, sarayın bininci odası." = "This is the palace's thousandth room" [Pronoun usage]
"Bu sarayın bininci odası" = "This palace's thousandth room" [Adjectival usage]
Note that the first is a complete sentence while the second is a fragment.
Phrases like "the France's tenth king" or "the Turkey's tallest mountain" do not occur in English; you must leave out "the" in each case to make them correct. The names of countries and cities almost never have "the" before them in English. (Yes, there are exceptions: "The Gambia," "The Hague," "the Vatican.") But in "This is the thousandth room of the palace," "the" is required in both places. I appreciate that it can be hard to know when to use "the" and when not to, but I hope I provided at least a little light.
Can we get out of "the" jargon in English translation, as we are not here to put right our knowledge of English. Sometimes, it is made mandatory to put "the" in the subject, other times putting "the" in the subjects considered criminal to be paid with the penalty. Be linient in handling such minor English aspects. This would be a motivation to learning for the non English speaking learners.