Why does it say that there will be a remnant in Har Tziyon?
Radak: Even though many of Yisrael were eradicated in exile, a large remnant will remain in Har Tziyon, from which they were exiled.
Malbim: After several nations who destroyed the land are eradicated, and memory of them ceases, there will be a remnant in Har Tziyon, and Yisraelim who were cast off will gather there little by little.
Why does it say "v'Hayah Kodesh"?
Radak: Yisrael will be Kodesh to Hashem. There will not be Arelim or Temei'im among them.
What are "Morasheihem"?
Rashi citing Targum Yonasan: The property of the nations that used to 'inherit' Yisrael (take over their property).
Radak: Yisrael will inherit (get back) what they initially inherited. Additionally, they will inherit their neighbors - the lands of Edom, Mo'av and Pelishtim.
