To what do these Mumim apply?
Rashi (like R. Yehudah, Kidushin 25b): All four mentioned in the Pasuk 1 apply both to the Gid (penis) and to the Beitzim (testicles).
Targum Yonasan: "Ma'uch" and "Kasus" refer [even 2 ] to the Beitzim, and "Natuk" and "Karus" to the Gid.
R. Eliezer ben Yakov (Kidushin 25b): All of them apply only to the Gid. 3
Presumably, he holds like R. Yosi in Kidushin 25b, and is not a new opinion.
Moshav Zekenim: Why do we forbid castrating via the Beitzim nowadays? The Halachah always follows R. Eliezer ben Yakov! Also, R. Yosi agrees that Nasuk and Karus do not apply to the Beitzim, and 'Nimuko Imo' (he had great reasons for his words)! We follow the Amora'im [against general rules about whom the Halachah follows]. Rava rules (Yevamos 75b, regarding people) like R. Meir (perhaps this should say 'R. Yehudah').
What is the difference between "Ma'uch", "Kasus", "Natuk" and "Karus"?
Rashi: They mean 'squashed by hand', 'crushed', 'severed' by hand, but still intact, and 'fragmented', 1 using an implement, respectively.
What does the ramifications of "uv'Artzechem Lo Sa'asu"?
Rashi: It is a prohibition against castrating any animal. 1
Seforno: After dealing with the blemishes that occur by themselves, which are confined to Kodshei Mizbe'ach, the Torah discusses inflicted blemishes, which are forbidden even in Chulin.
Seeing as the current prohibition has nothing to do with Eretz Yisrael (in which case it applies equally in Chutz la'Aretz), why does the Pasuk insert the word "uv'Artzechem"?
Rashi (from Chagigah 14b): To incorporate even Tamei species 1 in the prohibition of castration.
Moshav Zekenim (from Toras Kohanim): Since uv'Artzechem precedes Lo Sa'asu, we include Kol sheb'Artzechem 2 , we forbid everything - even a Ba'al Mum, birds and Tamei species - even in Chutz la'Aretz. It is forbidden even via Nochrim. 3
Rashi: 'Lerabos Kol Asher b'Artzechem'. Radvaz, Teshuvas Kesav Yad OC/YD 8:123 - since it does not depend on the land, we do not expound to exclude Chutz la'Aretz.
Moshav Zekenim: Also regarding "Even Maskis" (26:1), had it written b'Artzechem Lo Sitnu, we would forbid everywhere. Rather, it said "Lo Sitnu b'Artzechem" to exclude (and permit) in the Mikdash (Megilah 22b).
Moshav Zekenim citing the Rambam (Hilchos Isurei Bi'ah 16:13): One may not tell a Nochri to castrate a Jew's animal. If the Nochri bought it and castrated it, it is permitted [to buy it back], unless he schemed.
Bechoros 33b says that if one is liable for Ma'uch, all the more so for Kasus, which is greater. We do not punish based on a Kal v'Chomer!
Moshav Zekenim: Ein Onshin Min ha'Din applies only to learning s new matter. Here it is one matter, just we come to add (a greater level).
Why do we eat castrated lambs and Barburim Avusim (castrated fowl, which are fatter - Radak Melach im 1:5:3)? It should be forbidden, due to "Lo Sochal Kol To'evah" (what came through an Aveirah)!
Rosh, Moshav Zekenim #1: Since the Torah forbade it for a Korban, we infer that people may eat it.
Moshav Zekenim #2:"Lo Sochal Kol To'evah" applies only to an Aveirah that helped to prepare the food (cooking meat and milk, plowing with diverse species).