What kind of Ma'aser is the Pasuk talking about?
Rashi: It is talking about Ma'aser Sheini (which the Torah calls 'Kodesh') 1
See Sifsei Chachamim.
What are "t " and "mi'Peri ha'Eitz" referring to?
Rashi: "Mi'Zera ha'Aretz" is referring to Dagan (the five species of grain), 1 and "mi'Peri ha'Eitz", to wine and olive-oil - exclusively.
Hadar Zekenim (citing Toras Kohanim): "Mi'Zera ha'Aretz" includes everything eaten and seeded, e.g. garlic and cress. 2
Toras Kohanim (5:12): "Mi'Peri ha'Eitz" includes all tree fruits. However, since it says mi'Peri, we exclude some, e.g. carobs. 3
Wheat, barley, rye, oats and spelt.
Da'as Zekenim: From here, if one separated Ma'aser from sheaves, before it is called Degen, it is Ma'aser, even though one who separated Chalah before kneading, it is not Chalah.
Malbim (112): We exclude what is not so proper to eat. This is like the Ramban; others explain that this is a mere Asmachta.
What are the connotations of "la'Hashem hu"?
Rashi: It means that Hashem acquired it and commanded Yisrael to eat it at His Table in Yerushalayim. 1
Toras Kohanim expounds "mi'Zera ha'Aretz" to include Ma'aser of vegetables. The Gemara says that this is mid'Rabanan!
Moshav Zekenim: The verse is an Asmachta.