Why does it say "Ko Amar Hashem"?
Malbim: Now it discusses another punishment for their Simchah after the Churban. They danced to show Simchah, for they settled in Eretz Yisrael - "Madu'a Yarash Malkam Es Gad v'Amo b'Arav Yashav" (Yirmeyah 30:9), "Al Bik'am Haros ha'Gil'ad Lema'an Harchiv Es Gevulam" (Amos 1:13).
What is the significance of "Mach'acha Yad v'Rak'acha b'Ragel"?
Rashi: You did so for Simchah. Even though above (6:11) "Hake b'Chapecha u'Rka b'Raglecha ve'Emar He'ach" refers to mourning, there are matters done for mourning or Simchah, just they are done in different ways. Also flutes are used for a Kalah, and for a Mes! V'Rak'acha is an expression of trampling.
Radak: You rejoiced over the desolation of Eretz Yisrael, and clapped hands. This is like "v'Chol Etz ha'Sadeh Yimcha'u 1 Chaf" (Yeshayah 55:12), "va'Yaku Chaf va'Yomeru Yechi ha'Melech" (Melachim II, 11:12). Reka is stamping the foot on the ground for Simchah, i.e. dancing.
Radak: Mach'acha is Makor (infinitive). There is a Patach under the first letter of the root (Mem) because a guttural letter (Ches) follows it, like "uv'Shachatam Es Beneihem" (23:39), "Lefa'amo b'Machane Dan" (Shoftim 13:25). Normally, there is a Chirik, like "b'Shivri Lachem" (Vayikra 26:26), "b'Fischi Es Kivroseichem" (below, 37:13). "V'Rak'acha" has a Patach under the Reish, even though Kuf is not guttural, for parallel structure with Mach'acha.
What is "Shatecha"?
Rashi citing others: It is disgrace. The Targum of "va'Yivez Esav" (Bereishis 25:34) is v'Shat. Radak - you rejoice over their evil because you disgraced them in your Nefesh and heart.
Rashi: It is an expression of Shetef (gluttony).
